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Maya flipped 24 coins, each of which landed with either a head face-up

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Bunuel
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Maya flipped 24 coins, each of which landed with either a head face-up [#permalink] New post   21 Sep 2021, 03:00
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Maya flipped 24 coins, each of which landed with either a head face-up or a tail face up, hereafter referred to as an outcome of “heads” or “tails.”

If all the coins are fair, in that the probability of “heads” = probability of “tails” = \(\frac{1}{2}\) for every toss, which of the following events has the greatest probability?

A. Of the 24 tosses, the number of “heads” equals 11.
B. Of the 24 tosses, the number of “heads” equals 12.
C. Of the 24 tosses, the number of “tails” equals 14.
D. Of the 24 tosses, the number of “tails” is at most 3.
E. Of the 24 tosses, the number of “heads” is it least 22
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baruto
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Re: Maya flipped 24 coins, each of which landed with either a head face-up [#permalink] New post   25 Sep 2021, 12:08
Bunuel wrote:
Maya flipped 24 coins, each of which landed with either a head face-up or a tail face up, hereafter referred to as an outcome of “heads” or “tails.”

If all the coins are fair, in that the probability of “heads” = probability of “tails” = \(\frac{1}{2}\) for every toss, which of the following events has the greatest probability?

A. Of the 24 tosses, the number of “heads” equals 11.
B. Of the 24 tosses, the number of “heads” equals 12.
C. Of the 24 tosses, the number of “tails” equals 14.
D. Of the 24 tosses, the number of “tails” is at most 3.
E. Of the 24 tosses, the number of “heads” is it least 22


One of the ways to solve this is:
Since 24 coin is flipped, and probability of “heads” = probability of “tails” = \(\frac{1}{2}\) for every toss
Then highest probability should be getting half heads and half tails
That is 12 head/tail
Option B does that
Hence IMO B
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Maya flipped 24 coins, each of which landed with either a head face-up [#permalink] New post   25 Sep 2021, 21:33
P(Head) = P(Tail) = P(Total Toss)/2
Only condition matches is when P(H) = P(T) = P(24/2) = 12
Corrct Option : B

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Re: Maya flipped 24 coins, each of which landed with either a head face-up [#permalink] New post   15 Oct 2022, 11:13
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Given that all coins are fair and probability of “heads” = probability of “tails” = \(\frac{1}{2}\) and we need to find which of the following events has the greatest probability?

Since the coins are fair so at each and every toss P(H) = P(T) = \(\frac{1}{2}\)

So, irrespective of how many tosses we do, Number of Heads = Number of Tails = \(\frac{1}{2}\) * Number of tosses

=> After 24 tosses, Number of Heads = Number of Tails = \(\frac{1}{2}\) * Number of tosses = \(\frac{1}{2}\) * 24 = 12

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

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Re: Maya flipped 24 coins, each of which landed with either a head face-up [#permalink]
15 Oct 2022, 11:13
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