Five dice are thrown simultaneously. If the occurrence of 3, 4 or 5 in a single die is considered a success, find the probability of at least 3 successes.

Explanation

Let` X` denote the occurrence of` 3,4 or 5 `in a single die.
Then, `X f`ollows binomial distribution with` n=5`.

Let `p=` probability of getting `3,4 , or 5 `in a single die.


`p=frac{3}{6}=frac{1}{2} `

`q=1-frac{1}{2}=frac{1}{2} `

`P(X=r)=^{5} C_{r}(frac{1}{2})^{r}(frac{1}{2})^{5-r} `

P(text { at least }` 3 text { successes })=P(X geq 3) `

`=P(X=3)+P(X=4)+P(X=5) `

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