Question

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of a number of successes, find the probability distribution of the number of successes. Also, find the mean and variance of a number of successes.

Answer 1

Given : A die is tossed twice and ‘Getting a number greater than 4 ’ is considered a success.

To find : probability distribution of the number of successes and mean (μ) and variance (σ²)

Formula used :

When a die is tossed 4 times,

Total possible outcomes = 6² = 36

Getting a doublet is considered as a success

The possible doublets are (1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6)

Let p be the probability of success,

since the die is thrown 4 times, n = 4

x can take the values of 1,2,3,4

The probability distribution table is as follows,

The probability distribution table is as follows,

Mean = \(\frac{2}{3}\)

Variance = \(\frac{5}{9}\)