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# When a coin is flipped, the probability of getting heads is

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When a coin is flipped, the probability of getting heads is [#permalink]  13 Mar 2019, 12:10
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Question Stats:

78% (01:57) correct 21% (01:07) wrong based on 51 sessions
When a coin is flipped, the probability of getting heads is 0.5, and the probability of getting tails is 0.5 A coin is flipped 5 times.

 Quantity A Quantity B Probability of getting exactly 2 heads Probability of getting exactly 3 heads

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: When a coin is flipped, the probability of getting heads is [#permalink]  16 Mar 2019, 06:23
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Carcass wrote:
When a coin is flipped, the probability of getting heads is 0.5, and the probability of getting tails is 0.5 A coin is flipped 5 times.

 Quantity A Quantity B Probability of getting exactly 2 heads Probability of getting exactly 3 heads

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Since P(heads) = P(tails), we know that:
P(0 HEADS in 5 flips) = P(0 TAILS in 5 flips)
P(1 HEAD in 5 flips) = P(1 TAIL in 5 flips)
P(2 HEADS in 5 flips) = P(2 TAILS in 5 flips)
P(3 HEADS in 5 flips) = P(3 TAILS in 5 flips)
P(4 HEADS in 5 flips) = P(4 TAILS in 5 flips)
P(5 HEADS in 5 flips) = P(5 TAILS in 5 flips)

Now notice that getting 2 TAILS in 5 flips is exactly the same as getting 3 HEADS in 5 flips [if 2 flips are tails, then the other 3 flips must be heads]

So, we can write: P(2 HEADS in 5 flips) = P(2 TAILS in 5 flips) = = P(3 HEADS in 5 flips)

Cheers,
Brent
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Re: When a coin is flipped, the probability of getting heads is [#permalink]  09 Sep 2019, 18:50
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Carcass wrote:
When a coin is flipped, the probability of getting heads is 0.5, and the probability of getting tails is 0.5 A coin is flipped 5 times.

 Quantity A Quantity B Probability of getting exactly 2 heads Probability of getting exactly 3 heads

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

concise why that I thought about this one is reading the question as "what's the probability of getting exactly 2 heads vs getting exactly 2 tails" Well, both sides have equal probability, so clearly it's going to be the same.

I'd be curious about how to do the math if the question was a bit more nuanced but I don't think that would be on the GRE. Right now my only thought would be to make a table of all possible answers (denominator) and then count how many acceptable answers there are (numerator).
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Re: When a coin is flipped, the probability of getting heads is [#permalink]  28 Oct 2019, 19:56
In Magoosh, it,s a hard question not medium.
Re: When a coin is flipped, the probability of getting heads is   [#permalink] 28 Oct 2019, 19:56
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