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 : [tex]P(X=r) =^nC_r p^r q^{n-r}[/tex]
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
[tex]P(X=5) =^{30}C_5 (0.25)^5 (0.75)^{30-5}[/tex]
[tex]P(X=5) =\frac{30!}{5!(30-5)!} \times(0.25)^5 (0.75)^{30-5}[/tex]
[tex]P(X=5) =0.1047[/tex]
Hence the probability that exactly 5 are unable to complete the race is 0.1047
