Hugo plans to buy packs of baseball cards until he gets the card of his favorite player but he only has enough money to buy at most four packs. Suppose that each pack has a probability of 0.20 of containing the card Hugo is hoping for. Find the probability that it takes three or more packs to get the card of his favorite player.

Question

Mathematics

Reid Spears

25 October, 05:20

Hugo plans to buy packs of baseball cards until he gets the card of his favorite player but he only has enough money to buy at most four packs. Suppose that each pack has a probability of 0.20 of containing the card Hugo is hoping for. Find the probability that it takes three or more packs to get the card of his favorite player.

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Lucian · Answer 1

Step-by-step explanation:

This is an example of a geometric probability distribution because trials are repeated until the first success is gotten. Since each pack has a probability of 0.20 of containing the card Hugo is hoping for, it means that the probability of success, p = 0.2.

Let x represent the number of packs it takes to get the card of his favorite player. The the probability that it takes three or more packs to get the card of his favorite player is expressed as

P (x ≥ 3)

By using the geometric distribution calculator,

P (x ≥ 3) = 0.64