If a citizen of Ireland is selected at random, the probability they have red hair is...

If a citizen of Ireland is selected at random, the probability they have red hair is 0.11. If several citizens are selected, assume it is done one at a time with replacement and consecutive selections are independent of each other. n=6 citizens will be randomly selected.

14a) What is the probability all six citizens will have red hair?

14b) What is the probability at least one will have red hair?

14c) What is the probability the first four randomly selected citizens will have red hair and the last two will not?

14d) What is the probability exactly 4 of the 6 citizens will have red hair? Hints:
What is the difference between this question and the last one? How many different ways can 4 “reds” and 2 “not-reds” be ordered?

Expert Solution

a)

probability all six citizens will have red hair =(0.11)⁶ =0.0000018

b)

probability at least one will have red hair =P(none of them has red hair) =1-(1-0.11)⁶ =0.372578

c)

P(first 4 have red and last two will not) =(0.11)⁴*(1-0.11)² =0.000116

d)

number of ways to arrange 6 people so that 4 has red and 2 not =(₆C₄) =(6!/(4!*2!)) =15

therefore probability=15*(0.11)⁴*(1-0.11)² =0.001740

orchestra answered 2 years ago

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