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When tossed, a certain coin

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When tossed, a certain coin

by BTGmoderatorDC » Tue Dec 26, 2017 4:30 am

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When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2

Can some experts show the best solution in this problem?

OA B
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by elias.latour.apex » Tue Dec 26, 2017 6:00 am
The easiest solution is to realize that the first toss doesn't matter. Regardless of whether it comes up heads or tails, you are still on a good path. What is important is that the second and third toss match the first one. What are the chances that the second toss will match the first? Well, there is one chance out of two that it will come up the same. Similarly, the third toss has one chance out of two to come up the same. So the odds that both will occur are 1/2 times 1/2 or 1/4. That's answer choice (B).

An alternate solution is to calculate the chance that the coin will come up heads three times in a row. That chance is 1/2 * 1/2 * 1/2 or 1/8. Similarly, there is a 1/8 chance that tails will come up three times in a row. Once you add those two probabilities, you come up with 2/8, which reduces to 1/4. That's answer choice (B).
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by Scott@TargetTestPrep » Thu Sep 05, 2019 5:16 am
BTGmoderatorDC wrote:When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2

Can some experts show the best solution in this problem?

OA B
We need to determine the probability that a coin lands on the same side for all 3 tosses of the coin. This means that the 3-toss outcome will be either H-H-H or T-T-T.

P(T-T-T) = 1/2 x 1/2 x 1/2 = 1/8

P(H-H-H) = 1/2 x 1/2 x 1/2 = 1/8

Thus, the probability that the coin lands on the same side each time is 1/8 + 1/8 = 2/8 = 1/4.

Answer: B

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by [email protected] » Thu Sep 05, 2019 8:40 pm
Hi All,

We're told that a certain coin has equal probability of landing on either side and that the coin is tossed 3 times. We're asked for the probability that it will land on the same side all 3 times. This question can be approached in a couple of different ways. With certain GMAT questions, it's actually pretty easy to just 'brute force' the solution - simply map out the possibilities and answer the question that is asked.

Since we're tossing a coin 3 times, there are only 2^3 = 8 possible outcomes - and they would be (re: H = "heads", T = "tails")
HHH
HHT
HTH
THH

TTT
TTH
THT
HTT

Just 2 of the 8 options have the same outcome on all 3 tosses (HHH and TTT), so the answer to the question is 2/8 = 1/4

Final Answer: B

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Rich
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