Question

Review Problem 1.9 A cereal company puts a prize in 95% of their boxes. If you buy one box every week for a year, find the chance that you will collect at least 50 prizes.

Review Problem 1.10 Two cards are dealt from a well-shuffled deck. Find the probability that the first is an ace or the second is a jack.

Answer 1

1.9

Binomial with p = 0.95, q = 1-0.95 = 0.05

Total weeks in a year =52

For the chance that you will collect at least 50 prizes

n = 52, r = 50

Thus, required probability = ⁵²C₅₀*(0.95)⁵⁰*(0.05)² = 0.255

1.10

P(first ace or second jack) = P(first ace) + P(second jack) - P(first ace and second jack)

= 4/52 + 4/52 - 0 (as these are indpendent events)

= 2/13