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

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Math Expert
Joined: 02 Sep 2009
Posts: 60545
An unfair coin comes up heads 60% of the time and tails 40% of the tim  [#permalink]

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02 Dec 2019, 01:20
00:00

Difficulty:

45% (medium)

Question Stats:

71% (01:58) correct 29% (01:45) wrong based on 17 sessions

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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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Joined: 21 Dec 2017
Posts: 2
Re: An unfair coin comes up heads 60% of the time and tails 40% of the tim  [#permalink]

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02 Dec 2019, 01:42
1
HHHTT
6^3/10^3 * 4^3/10^3 * 5!/3!*2!
= 6^3/5^4.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5701
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: An unfair coin comes up heads 60% of the time and tails 40% of the tim  [#permalink]

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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. $$\frac{6^3}{5^4}$$

Are You Up For the Challenge: 700 Level Questions
Re: An unfair coin comes up heads 60% of the time and tails 40% of the tim   [#permalink] 02 Dec 2019, 02:22
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