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For one toss of a certain coin, the probability that the outcome is he

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For one toss of a certain coin, the probability that the outcome is he [#permalink] New post   30 Mar 2022, 05:13
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For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

A. \((0.6)^5\)

B. \(2(0.6)^4\)

C. \(3(0.6)^4\)

D. \(4(0.6)^4(0.4) + (0.6)^5\)

E. \(5(0.6)^4(0.4) + (0.6)^5\)
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Re: For one toss of a certain coin, the probability that the outcome is he [#permalink] New post   07 Apr 2022, 03:09
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Given: For one toss of a certain coin, the probability that the outcome is heads is 0.6.
Asked: If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

The probability that the outcome will be heads at least 4 times = The probability that the outcome will be heads 4 times + The probability that the outcome will be heads 5 times = 5C4*(.6)^4*(.4) + 5C5*(.6)^5 = 5(.6)^4(.4) + (.6)^5

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Re: For one toss of a certain coin, the probability that the outcome is he [#permalink] New post   13 Aug 2022, 06:16
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Since there are only two possible outcomes, we can apply binomial probability distribution.

success = p = 0.6
failure = q = 0.4

P(at least 4 heads) = P(4 heads) + P(5 heads)
= 5C4\(p^4\)*\(q^1\) + 5C5\(p^5\)*\(q^0\)
= 5\((0.6)^4\)(0.4) + \((0.6)^5\)
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Re: For one toss of a certain coin, the probability that the outcome is he [#permalink]
13 Aug 2022, 06:16
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