A bag contains 6 marbles. Three of the marbles are red. Each time you draw a marble out of the bag at random you replace it. You do this 4 times. Estimate the probability of at least 2 of the marbles being red.
Explain too! Thanks
Probability with Replacement help!?
2019-03-10 12:45 am
回答 (1)
2019-03-10 1:27 am
P(Red in each time) = 3/6 = 1/2
P(Not Red in each time) = 1 - (1/2) = 1/2
Drawing a marble for 4 times with replacement, P(at least 2 Red)
= 1 - P(0 Red) - P(1 Red)
= 1 - P(4 Not Red) - P(1 Red)
= 1 - (1/2)⁴ - ₄C₁(1/2)(1/2)³
= 1 - (1/16) - (4!/1!3!)(1/16)
= 1 - (1/16) - (4/16)
= 11/16
OR:
Drawing a marble for 4 times with replacement, P(at least 2 Red)
= P(2 Red) + P(3 Red) + P(4 Red)
= ₄C₂(1/2)²(1/2)² + ₄C₃(1/2)³(1/2) + (1/2)⁴
= (4!/2!2!)(1/16) + (4!/3!1!)(1/16) + (1/16)
= (6/16) + (4/16) + (1/16)
= 11/16
P(Not Red in each time) = 1 - (1/2) = 1/2
Drawing a marble for 4 times with replacement, P(at least 2 Red)
= 1 - P(0 Red) - P(1 Red)
= 1 - P(4 Not Red) - P(1 Red)
= 1 - (1/2)⁴ - ₄C₁(1/2)(1/2)³
= 1 - (1/16) - (4!/1!3!)(1/16)
= 1 - (1/16) - (4/16)
= 11/16
OR:
Drawing a marble for 4 times with replacement, P(at least 2 Red)
= P(2 Red) + P(3 Red) + P(4 Red)
= ₄C₂(1/2)²(1/2)² + ₄C₃(1/2)³(1/2) + (1/2)⁴
= (4!/2!2!)(1/16) + (4!/3!1!)(1/16) + (1/16)
= (6/16) + (4/16) + (1/16)
= 11/16
收錄日期: 2021-05-01 22:35:14
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