## Book: Mathematics Part-II

### Chapter: 13. Probability

#### Subject: Maths - Class 12th

##### Q. No. 5 of Exercise 13.4

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##### Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as(i) number greater than 4(ii) six appears on at least one die

Given: A die is tossed two times.

When a die is tossed two times then the number of observations will be (6 × 6) = 36.

Now, let X is a random variable which represents the success.

(i) Here success is given as the number greater than 4.

Now

P(X = 0) = P(number ≤ 4 in both tosses) P(X = 1) = P(number ≤ 4 in first toss and number ≥ 4 in second case) + P(number ≥ 4 in first toss and number ≤ 4 in second case) is: P(X = 2) = P(number ≥ 4 in both tosses) Hence, the required probability distribution is,

 X 0 1 2 P(X) 4/9 4/9 1/9

(ii) Here success is given as six appears on at least one die.

Now

P(X = 0) = P(six does not appear on any of die) P(X = 1) = P(six appears atleast once of the die) Hence, the required probability distribution is,

 X 0 1 P(X) 25/36 5/18

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