A dice is rolled twice. Find the probability distribution of number of successes if : A number greater than 4 is to be considered as success.

Explanation

When a die is tossed two times, we obtain `(6` times ` 6)=36 ` number of observations.

Let `X` be the random variable, which represents the number of successes.

Here, success refers to the number greater than `4` .

`P(X=0)=P `(number less than or equal to `4` on both the tosses )`=frac{4}{6} times frac{4}{6}=frac{16}{36}=frac{4}{9}`

`P(X=1)=P` (number less than or equal to `4 `on first toss and greater than `4 ` on second toss) +`P `(number greater than `4` on first toss and less than or equal to ` 4` on second toss)


`=frac{4}{6} times frac{2}{6}+frac{4}{6} times frac{2}{6}=frac{8}{36}+frac{8}{36}=frac{16}{36}=frac{4}{9}`


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