Keisha decides to roll a number cube until she gets a 6. Let X = the number of rolls until she rolls a 6.What is the probability that Keisha gets her first 6 before her 3rd roll? Round to 3 decimal places.Recall: P(X = k) = (1 – p)k–1p

A 6 has probability 1/6 on each roll, so the probability of not getting a 6 on one roll is 5/6. Getting the first 6 before the 3rd roll means getting it on roll 1 or roll 2; equivalently, she does not miss on both of the first two rolls. Thus the probability is 1 − (5/6)² = 11/36 ≈ 0.306, so the answer is 0.306.

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