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An unfair coin comes up heads 60% of the time and tails 40% of the tim

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Bunuel
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An unfair coin comes up heads 60% of the time and tails 40% of the tim [#permalink] New post   02 Dec 2019, 01:20
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An unfair coin comes up heads 60% of the time and tails 40% of the time when it is tossed. What is the probability of getting exactly three heads on five tosses of this coin?

A. \(\frac{10}{32}\)

B. \(\frac{27}{125}\)

C. \(\frac{2^33^3}{5^5}\)

D. \(\frac{3}{5}\)

E. \(\frac{6^3}{5^4}\)


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Re: An unfair coin comes up heads 60% of the time and tails 40% of the tim [#permalink] New post   02 Dec 2019, 01:42
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6^3/10^3 * 4^3/10^3 * 5!/3!*2!
= 6^3/5^4.
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Re: An unfair coin comes up heads 60% of the time and tails 40% of the tim [#permalink] New post   02 Dec 2019, 02:22
total fair ways ; 5!/3!*2! ; 10
and for heads and tails ; 5c3*(.6)^3 *(.4)^2*5c2
total P of exactly three heads on five tosses ; 5c3*(.6)^3 *(.4)^2*5c2/10
solve =
\(\frac{6^3}{5^4}\)

IMO E

Bunuel wrote:
An unfair coin comes up heads 60% of the time and tails 40% of the time when it is tossed. What is the probability of getting exactly three heads on five tosses of this coin?

A. \(\frac{10}{32}\)

B. \(\frac{27}{125}\)

C. \(\frac{2^33^3}{5^5}\)

D. \(\frac{3}{5}\)

E. \(\frac{6^3}{5^4}\)


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Re: An unfair coin comes up heads 60% of the time and tails 40% of the tim [#permalink] New post   31 Jan 2022, 03:05
60℅=3/5

So, 3 times heads and 2 times heads => (3/5)*(3/5)*(3/5)*(2/5)*(2/5)
Now Here order matters because first throw can result in tail and second throw can result in head and so on......

So We will multiply by 5!/(3!*2!)

Thus answer E.

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Re: An unfair coin comes up heads 60% of the time and tails 40% of the tim [#permalink]
31 Jan 2022, 03:05
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