Question

The probability of a randomly drawn individual having blue eyes is 0.51. A) What is the probability that seven people drawn at random all have blue​ eyes?
​(b) What is the probability that one of the sample of seven has blue​ eyes?

Answer 1

prob(b) = .51
prob(x) = .49 , where x is "not blue eyes"

one such case could be
xxbxxxx , which would be (.51)(.49^6)
but there are 7 such cases, so

prob(your event) = 7(.51)(.49^6)
= ....

in stats notation:
C(7,1)(.51)(.49)^6

Answer 2

I put the answer to part a) as 0.51^7 which gave me answer of 8.9741 to 4 dp.

For part B your working out gives an answer of 0.049 to 4 dp is this correct?

Answer 3

I only answered part b) since a) is very simple

a) would be .51^7 = .0089741

I have no idea how yo got 8.9741, the digits are the same, but no probability can be greater than 1.

for b) the answer correct to 4 decimals is
.0494, your is correct only to 3 decimals