Answer
See below
Work Step by Step
The standard formula: $P(number-of-successes)=\frac{n!}{(n-k)!k!}.p^k(1-p)^{n-k}$
Substituting $p=0.025,n=8,k=0$ we have:
$P(0)=\frac{8!}{(8-0)!0!}.(0.025)^0(1-0.025)^{8-0}\approx0.8167$
Substituting $p=0.025,n=8,k=0$ we have:
$P(1)=\frac{8!}{(8-1)!1!}.(0.025)^1(1-0.025)^{8-1}\approx0.1675$
Substituting $p=0.025,n=8,k=2$ we have:
$P(2)=\frac{8!}{(8-2)!2!}.(0.025)^2(1-0.025)^{8-2}\approx0.015$
Substituting $p=0.025,n=8,k=3$ we have:
$P(3)=\frac{8!}{(8-3)!3!}.(0.025)^3(1-0.025)^{8-3}\approx0.00077$
Substituting $p=0.025,n=8,k=4$ we have:
$P(4)=\frac{8!}{(8-4)!4!}.(0.025)^4(1-0.025)^{8-4}\approx0.0000247$
Substituting $p=0.025,n=8,k=5$ we have:
$P(5)=\frac{8!}{(8-5)!5!}.(0.025)^5(1-0.025)^{8-5}\approx0.00000051$
Substituting $p=0.025,n=8,k=6$ we have:
$P(6)=\frac{8!}{(8-6)!6!}.(0.025)^6(1-0.025)^{8-6}\approx0.0000000065$
Substituting $p=0.025,n=8,k=7$ we have:
$P(7)=\frac{8!}{(8-7)!7!}.(0.025)^7(1-0.025)^{8-}\approx0.0000000000476$
Substituting $p=0.025,n=8,k=8$ we have:
$P(8)=\frac{8!}{(8-8)!8!}.(0.025)^8(1-0.025)^{8-8}\approx0.000000000000153$
The most likely number of successes is 0.
