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.

Question

asked Sep 17, 2019 78.0k views

1 Answer

PKumar · Answer 1 · 2019-09-24T07:13:09+0000

Answer:

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
total number of trials,
number of success and
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%