Question

25% of all who enters a race do not complete. 30 haveentered.

Answer 1

Answer:

The probability that exactly 5 are unable to complete the  race is 0.1047

Step-by-step explanation:

We are given that 25% of all who enters a race do not complete.

30 have entered.

what is the probability that exactly 5 are unable to complete the  race?

So, We will use binomial

Formula : $P(X=r) =^nC_r p^r q^{n-r}$

p is the probability of success i.e. 25% = 0.25

q is the probability of failure =  1- p  = 1-0.25 = 0.75

We are supposed to find the probability that exactly 5 are unable to complete the  race

n = 30

r = 5

$P(X=5) =^{30}C_5 (0.25)^5 (0.75)^{30-5}$

$P(X=5) =\frac{30!}{5!(30-5)!} \times(0.25)^5 (0.75)^{30-5}$

$P(X=5) =0.1047$

Hence the probability that exactly 5 are unable to complete the  race is 0.1047