A pair of dice is thrown 6 times. If getting a total of 7 is considered a success , find the probability of atleast five successes.

Explanation

Let `X` be the number of successes in `6` throws of the two dice.

Probability of success=Probability of getting a total of `9`

`=`Probability of getting `(3,6),(4,5),(5,4),(6,3)` out of `36` outcomes.

`p=frac{4}{36}=frac{1}{9},q=1-p=frac{8}{9}`and `n=6`

`X` follows a binomial distribution with `n=6,p=frac{1}{9}and \q=frac{8}{9}`
`P(X=r)=^{6} C_{r}(frac{1}{9})^{r}(frac{8}{9})^{6-r}`


The required probability` = `Probability of at least `5` successes

`=P(X geq 5) `

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