Binomial Distribution

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JEE Main 2013

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

17/ 3^{5}

(B)

13/ 3^{5}

(C)

11/ 3^{5}

(D)

10/ 3^{5}

JEE Main 2007

LEVELJEE Main

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

(A)

28/256

The mean and variance of a random variable $X$ having binomial distribution are 4 and 2 respectively, then $P (X = 1)$ is

A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is

One hundred identical coins, each with probability, $p$ , of showing up heads are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins, then the value of $p$ is

(A)

1/2

(B)

49/101

(C)

50/101

(D)

51/101

JEE Advanced 1980

LEVELBoard

The probability that an event $A$ happens in one trial of an experiment is $0.4$ . Three independent trials of the experiment are performed. The probability that the event $A$ happens at least once is

(A)

0.936

(B)

0.784

(C)

0.904

A man takes a step forward with probability 0.4 and backwards with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.

JEE Advanced 1993

LEVELJEE Main

Numbers are selected at random, one at a time, from the two-digit numbers 00, 01, 02, ..., 99 with replacement. An event $E$ occurs if only if the product of the two digits of a selected number is 18. If four numbers are selected, find probability that the event $E$ occurs at least 3 times.

JEE Advanced 1991

LEVELBoard

If the mean and the variance of a binomial variate $X$ are 2 and 1 respectively, then the probability that $X$ takes a value greater than one is equal to .........

JEE Advanced 1989

LEVELJEE Main

Suppose the probability for $A$ to win a game against $B$ is 0.4. If $A$ has an option of playing either a "best of 3 games" or a "best of 5 games" match against $B$ , which option should be choose so that the probability of his winning the match is higher? (No game ends in a draw).

JEE Main 2019 (08 April Shift 2)

LEVELBoard

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :

JEE Main 2019 (10 April Shift 2)

LEVELBoard

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :

JEE Main 2019 (12 April)

LEVELJEE Main

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 4/5, then the probability that he is unable to solve less than two problems is :

(A)

(316/25) (4/5)^{48}

(B)

(54/5) (4/5)^{49}

(C)

(164/25) (1/5)^{48}

(D)

(201/5) (1/5)^{49}

JEE Main 11 Jan 2019 (Evening)

LEVELJEE Main

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If $X$ be the number of white balls drawn; then $(\frac{mean of X}{Standard deviation of X})$ is equal to:

(A)

32

(B)

(C)

\frac{4 3}{3}

(D)

43

JEE Main 2020 - 9 Jan (Morning)

LEVELJEE Main

In a bag there are 20 cards 10 names $A$ and another 10 names $B$ . Cards are drawn randomly one by one with replacement then find probability that second $A$ comes before third $B$ .

JEE Main 2021 (27 July Shift 2)

LEVELJEE Main

A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. The smallest value of $n$ , so that the probability of guessing at least ' $n$ ' correct answers is less than $1/2$ , is

JEE Main 2021 (24 February Shift 1)

LEVELJEE Main

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :

(A)

\frac{3}{16}

(B)

\frac{1}{2}

(C)

\frac{5}{16}

(D)

\frac{1}{32}

JEE Main 2021 (26 February Shift 1)

LEVELJEE Main

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is :

(A)

\frac{15}{2 ^{12}}

(B)

\frac{15}{2 ^{13}}

(C)

\frac{15}{2 ^{14}}

(D)

\frac{15}{2 ^{8}}

JEE Main 2021 (March)

LEVELJEE Main

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to:

(A)

32/625

(B)

80/243

(C)

40/243

(D)

128/625

JEE Main 2022 (24 June Shift 1)

LEVELJEE Main

If a random variable $X$ follows the Binomial distribution $B (33, p)$ such that $3 P (X = 0) = P (X = 1)$ , then the value of $\frac{P ( X = 15 )}{P ( X = 18 )} - \frac{P ( X = 16 )}{P ( X = 17 )}$ is equal to

\frac{120}{1331}

(D)

\frac{1088}{1089}

JEE Main 2022 (24 June Shift 2)

LEVELJEE Main

In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability $\frac{3}{4}$ and the remaining 6 questions correctly with probability $\frac{1}{4}$ . If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is $\frac{27 k}{4 ^{10}}$ , then $k$ is equal to ____.

JEE Main 2022 (27 June Shift 1)

LEVELJEE Main

Let $X$ be a random variable having binomial distribution $B (7, p)$ . If $P (X = 3) = 5 P (X = 4)$ , then the sum of the mean and the variance of $X$ is:

(A)

\frac{105}{16}

(B)

\frac{7}{16}

(C)

\frac{77}{36}

(D)

\frac{49}{16}

JEE Main 2022 (26 July Shift 1)

LEVELJEE Main

The mean and variance of a binomial distribution are $α$ and $\frac{α}{3}$ respectively. If $P (X = 1) = \frac{4}{243}$ , then $P (X = 4 or 5)$ is equal to:

(A)

\frac{5}{9}

(B)

\frac{64}{81}

(C)

\frac{16}{27}

(D)

\frac{145}{243}

JEE Main 2022 (26 July Shift 2)

LEVELJEE Main

Let $X$ be a binomially distributed random variable with mean 4 and variance $\frac{4}{3}$ . Then $54 P (X \leq 2)$ is equal to

(A)

\frac{73}{27}

(B)

\frac{146}{27}

(C)

\frac{146}{81}

(D)

\frac{126}{81}

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P(X=1) is

A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is

A man takes a step forward with probability 0.4 and backwards with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to .........

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 4/5, then the probability that he is unable to solve less than two problems is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In a bag there are 20 cards 10 names A and another 10 names B. Cards are drawn randomly one by one with replacement then find probability that second A comes before third B.

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is :

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If a random variable X follows the Binomial distribution B(33,p) such that 3P(X=0)=P(X=1), then the value of P(X=18)P(X=15)​−P(X=17)P(X=16)​ is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let X be a random variable having binomial distribution B(7,p). If P(X=3)=5P(X=4), then the sum of the mean and the variance of X is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The mean and variance of a binomial distribution are α and 3α​ respectively. If P(X=1)=2434​, then P(X=4 or 5) is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let X be a binomially distributed random variable with mean 4 and variance 34​. Then 54P(X≤2) is equal to

The mean and variance of a random variable $X$ having binomial distribution are 4 and 2 respectively, then $P (X = 1)$ is

If the mean and the variance of a binomial variate $X$ are 2 and 1 respectively, then the probability that $X$ takes a value greater than one is equal to .........

In a bag there are 20 cards 10 names $A$ and another 10 names $B$ . Cards are drawn randomly one by one with replacement then find probability that second $A$ comes before third $B$ .

If a random variable $X$ follows the Binomial distribution $B (33, p)$ such that $3 P (X = 0) = P (X = 1)$ , then the value of $\frac{P ( X = 15 )}{P ( X = 18 )} - \frac{P ( X = 16 )}{P ( X = 17 )}$ is equal to

Let $X$ be a random variable having binomial distribution $B (7, p)$ . If $P (X = 3) = 5 P (X = 4)$ , then the sum of the mean and the variance of $X$ is:

The mean and variance of a binomial distribution are $α$ and $\frac{α}{3}$ respectively. If $P (X = 1) = \frac{4}{243}$ , then $P (X = 4 or 5)$ is equal to:

Let $X$ be a binomially distributed random variable with mean 4 and variance $\frac{4}{3}$ . Then $54 P (X \leq 2)$ is equal to