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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.

User Wspeirs
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1 Answer

1 vote

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
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%

User PKumar
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