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Marco tosses a coin four times. What is the probability that he gets heads exactly twice?

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by VJesus12 » Thu Jul 30, 2020 8:55 am
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Marco tosses a coin four times. What is the probability that he gets heads exactly twice?

(A) 1/4
(B) 3/8
(C) 7/16
(D) 1/2
(E) 5/8

[spoiler]OA=B[/spoiler]

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Re: Marco tosses a coin four times. What is the probability that he gets heads exactly twice?

by Scott@TargetTestPrep » Wed Aug 05, 2020 10:03 am
VJesus12 wrote: ↑
Thu Jul 30, 2020 8:55 am
 Marco tosses a coin four times. What is the probability that he gets heads exactly twice?

(A) 1/4
(B) 3/8
(C) 7/16
(D) 1/2
(E) 5/8

[spoiler]OA=B[/spoiler]

Solution:

If a coin is tossed four times and exactly two times are heads, then the other two times must be tails. The probability of getting two heads and two tails, i.e., HHTT, in that order, is ½ x ½ x ½ x ½ = 1/16. However, since the two heads and two tails can be arranged in 4! / (2!2!) = 24/4 = 6 ways, the overall probability that Marco gets heads exactly twice is 1/16 x 6 = 6/16 = 3/8.

Answer: B

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