Question

Find the probability of no failures in five trials of a binomial experiment in which the probability of success is 30%. Round to the nearest tenth of a percent.

Answer 1

The probability of no failures in five trials will be 0.2%

Explanation:

The binomial distribution formula is.....

`P= ^nC_(r) (p)^r (1-p)^n^-^r` , where
`n=` total number of trials,
`r=` number of success and
`p=` probability of success.

Here,
`n= 5` and
`p= 30\%= 0.30`

Now "probability of no failures" means probability of all success. So here,
`r=5`

Thus......

`P= ^5C_(5)(0.30)^5(1-0.30)^5^-^5\\ \\ P=1(0.30)^5(0.70)^0\\ \\ P=0.00243=0.243\%\approx 0.2\%`

(Rounding to the nearest tenth of a percent)

So, the probability of no failures in five trials will be 0.2%