CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. M.P.Keshari

Probability

Q.2. Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Find the probability distribution of number of aces.

Solution :

Do yourself. [Ans. of Q.1. above]

Q.3. A pair of dice is tossed twice. If the random variable X is defined as the number of doublets, find the probability distribution of X.

Solution :

X can take the values 0, 1 and 2.
Let E denote the event of getting a doublet. Then
P(E) = 6/36 = 1/6 and P(not E) = 1 – 1/6 = 5/6.
Now, P(X = 0) = P(not E1 & not E2)
= P(not E₁).P(not E₂)
= (5/6)(5/6) = 25/36.
P(X = 1) = P(E1 & not E₂ or not E₁ & E₂)
= P(E₁ & not E₂) + P(not E1 & E2)
= P(E₁).P(not E₂) + P(not E₁).P(E₂)
= (1/6)(5/6) + (5/6)(1/6)
= 10/36.
P(X = 2) = P(E₁E₂) = P(E₁).P(E₂) = (1/6)(1/6) = 1/36.
Hence, the required probability distribution is

Q.4. Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as a number less than 3. Also find the mean and the variance of the distribution.

Solution :

Let A be the event of getting a number < 3 on a die.
Then P(A) = 2/6 = 1/3. P(Not A) = 1 – 1/3 = 2/3.
X = 0, 1, 2.
P(X = 0) = P(Not A)P(Not A) = 2/3×2/3 = 4/9.