If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Jun 18, 2022 10:58 pm

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If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32

OA E

Source: GMAT Prep

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

Re: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times,

by regor60 » Mon Jun 27, 2022 10:09 am

The question is asking for the probability of a set of outcomes which occur in a specific order.

Since each toss is independent of the other and each face has a 1/2 chance of appearing the probability is [spoiler]1/32, E[/spoiler]

If the question had asked for probability of 3 heads and 2 tails occurring in 5 tosses, then would need to consider all orders that produce the result

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Re: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times,

by Brent@GMATPrepNow » Mon Jun 27, 2022 10:37 am

BTGmoderatorDC wrote: ↑
Sat Jun 18, 2022 10:58 pm
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32

OA E

Source: GMAT Prep

We want P(heads on 1st AND heads on 2nd AND heads on 3rd AND tails on 4th AND tails on 5th)
= P(heads on 1st) x P(heads on 2nd) x P(heads on 3rd) x P(tails on 4th) x P(tails on 5th)
= 1/2 x 1/2 x 1/2 x 1/2 x 1/2
= 1/32

Answer: E

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8189; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times,

by Scott@TargetTestPrep » Fri Jan 27, 2023 8:24 am

BTGmoderatorDC wrote: ↑
Sat Jun 18, 2022 10:58 pm
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32

OA E

Source: GMAT Prep

The probability that the first 3 flips are heads and last 2 flips are tails is:

P(HHHTT) = (1/2)^5 = 1/32.

Answer: E

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