Question

9. A set contains a large number of integers. How many integers must you select so that the probability of selecting at least one odd integer is at least 0.92 ?

Answer 1

P(an odd number) = 0.5

P(an even number) = 0.5

Let n be the number of integers needed so that probability of selecting at least one odd integer is at least 0.92

P(selecting at least one odd integer) = 1 - P(selecting all even integers)

0.92 = 1 - 0.5ⁿ

0.5ⁿ = 0.08

n x log 0.5 = log 0.08

n = log 0.08/log0.5

n = 3.64

$\approx$ 4