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?
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
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?
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
To find the probability of all seven people having blue eyes, we need to multiply the individual probabilities of each person having blue eyes. Since each person is chosen at random and the probability of having blue eyes is 0.51, the probability of an individual having blue eyes is 0.51.
- (a) To find the probability of all seven people having blue eyes, we multiply the probability of each person having blue eyes together:
P(7 people having blue eyes) = P(1st person has blue eyes) * P(2nd person has blue eyes) * ... * P(7th person has blue eyes)
P(7 people having blue eyes) = 0.51 * 0.51 * 0.51 * 0.51 * 0.51 * 0.51 * 0.51
- (b) Alternatively, to find the probability that at least one person out of seven has blue eyes, we can calculate the complement of the event that none of the seven people have blue eyes and subtract it from 1.
P(at least one person having blue eyes) = 1 - P(no one has blue eyes)
To find the probability of no one having blue eyes, we multiply the probability of each person not having blue eyes together:
P(no one has blue eyes) = P(1st person not having blue eyes) * P(2nd person not having blue eyes) * ... * P(7th person not having blue eyes)
Since the probability of an individual not having blue eyes is 1 - 0.51 = 0.49, we can calculate:
P(no one has blue eyes) = 0.49 * 0.49 * 0.49 * 0.49 * 0.49 * 0.49 * 0.49
Finally, we can substitute this value into the equation for the probability of at least one person having blue eyes:
P(at least one person having blue eyes) = 1 - P(no one has blue eyes)