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Probability with discrete random variables

AP.STATS: VAR‑5 (EU), VAR‑5.A (LO), VAR‑5.A.1 (EK), VAR‑5.A.2 (EK), VAR‑5.A.3 (EK) CCSS.Math: HSS.MD.A.1
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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 4 packs. Suppose that each pack has probability 0, point, 2 of containing the card Hugo is hoping for.
Let the random variable X be the number of packs of cards Hugo buys. Here is the probability distribution for X:
X, equals, \#, start text, space, o, f, space, p, a, c, k, s, end text1234
P, left parenthesis, X, right parenthesis0, point, 20, point, 160, point, 1280, point, 512
What is the probability that Hugo buys at most 3 packs of cards?
P, left parenthesis, start text, a, t, space, m, o, s, t, space, end text, 3, start text, space, p, a, c, k, s, end text, right parenthesis, equals
  • Your answer should be
  • an exact decimal, like 0, point, 75