The probability distribution of number of doublets in three throws of a pair of dice is Option 1: x, 0, 1, 2, 3, P(X=x), 125/216, 75/216, 15/216, 1/216 Option 2: x, 0, 1, 2, 3, P(X=x), 75/216, 125/216, 1/216, 15/216 Option 3: x, 0, 1, 2, 3, P(X=x), 1/216, 75/216, 15/216, 125/216 Option 4: x, 0, 1, 2, 3, P(X=x), 1/216, 15/216, 75/216, 125/216

Answer: x, 0, 1, 2, 3, P(X=x), 125/216, 75/216, 15/216, 1/216. Solution: Probability of a doublet in one throw of two dice: p = 6/36 = 1/6. Using binomial distribution with n=3: P(X=k) = 3k(1/6)^k(5/6)^(3-k). P(0)=125/216,\ P(1)=75/216,\ P(2)=15/216,\ P(3)=1/216.

Algebra

Probability

Easy

The probability distribution of number of doublets in three throws of a pair of dice is

$x$	0	1	2	3
$P(X=x)$	125/216	75/216	15/216	1/216

$x$	0	1	2	3
$P(X=x)$	75/216	125/216	1/216	15/216

$x$	0	1	2	3
$P(X=x)$	1/216	75/216	15/216	125/216

$x$	0	1	2	3
$P(X=x)$	1/216	15/216	75/216	125/216

✅ Correct Option: 1

Probability of a doublet in one throw of two dice: $p = \frac{6}{36} = \frac{1}{6}$ .

Using binomial distribution with $n=3$ :

$P(X=k) = \binom{3}{k}\left(\frac{1}{6}\right)^k\left(\frac{5}{6}\right)^{3-k}$ .

$P(0)=\frac{125}{216},\ P(1)=\frac{75}{216},\ P(2)=\frac{15}{216},\ P(3)=\frac{1}{216}$ .

2022: 25 May Shift 1

Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

2025: 15 May Shift 1

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution:

(A) The number of trials is indefinitely large.

(B) The probability of success for each trial is indefinitely small.

(D) The probability of success for each trial is indefinitely large.

Choose the correct answer from the options given below:

2025: 3 June Shift 1

The probability that a leap year selected at random will have 53 Mondays is

2025: 15 May Shift 2

If a random variable $X$ has the following probability distribution:

X	0	1	2	3	4
P(X)	k	2k	3k	k²	6k²

, then

Match List-I with List-II

List-I	List-II
(A) k	(I) 3/7
(B) $P(X < 2)$	(II) 6/49
(C) $P(X > 3)$	(III) 1/7
(D) $P(2 \leq X \leq 3)$	(IV) 22/49

Choose the correct answer from the options given below:

2026: 19 May Shift 1

Two thirds of the students in a class are boys and the rest are girls. It is known that the probability of a girl getting a first class is 0.25 and that of a boy getting a first class is 0.28, then the probability that a student chosen at random will get first class marks in the subject is

2026: 22 May Shift 1

The sum and the product of the mean and variance of binomial distribution are 1.8 and 0.8 respectively. The probability of atleast one success is:

The probability distribution of number of doublets in three throws of a pair of dice is

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