Book: RD Sharma - Mathematics (Volume 2)
Chapter: 33. Binomial Distribution
Subject: Maths - Class 12th
Q. No. 48 of Exercise 33.1
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A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
Given that, a pair of dice is thrown 4 times.
And a doublet is considered as a success.
Let p be the probability of getting a doublet in a throw of a pair of dice.
Since, there are 36 possible outcomes in total. {(1, 1), (1, 2), (1, 3), …, (1, 6), ..., (2, 6), …, (6 ,6)}
And the 6 possible doublets in 36 outcomes. {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
So,
And also, p + q = 1
⇒ q = 1 – p
Let X denote a random variable representing a number of doublets (successes) out of 4 throws.
So, Binomial distribution of getting r successes out of 4 throws is given by
P (X = r) = nCrprqn-r
Here, n = 4.
Now, substituting values of n, p and q in the formula P (X = r). We get
…(i)
We need to find the probability distribution of the number of successes.
The probability of 0 success in 4 throws is given by,
Probability = P (X = 0)
Put r = 0 in (i),
The probability of 1 success in 4 throws is given by,
Probability = P (X = 1)
Put r = 1 in (i),
The probability of 2 successes in 4 throws is given by,
Probability = P (X = 2)
Put r = 2 in (i),
The probability of 3 successes in 4 throws is given by,
Probability = P (X = 3)
Put r = 3 in (i),
The probability of 4 successes in 4 throws is given by,
Probability = P (X = 4)
Put r = 4 in (i),
Thus, the probability distribution is
