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How many times was a fair coin tossed?

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How many times was a fair coin tossed?

by swerve » Wed Nov 01, 2017 9:21 am
How many times was a fair coin tossed?

(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)
(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.

The OA is D.

I need help with this DS question. Please, can any expert explain it for me? Thanks.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Nov 01, 2017 8:25 pm
swerve wrote:How many times was a fair coin tossed?

(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)
(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.

The OA is D.

I need help with this DS question. Please, can any expert explain it for me? Thanks.
(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8).

Since the given probability of getting all the heads = 1/8 = (1/2)^3, it implies that the coin is tossed 3 times for this case. Thus, the number of time the coin is tossed = 3 + 4 = 7 times. Sufficient.

(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.

Since the given probability of getting all the heads = 1/128 = (1/2)^7, it implies that the coin is tossed 7 times. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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