John flips a coin 4 times. What is the probability

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

John flips a coin 4 times. What is the probability

by M7MBA » Sat Dec 23, 2017 3:37 am

John flips a coin 4 times. What is the probability that he gets heads on at least one of the four flips?

(A) 1/16
(B) 1/4
(C) 1/2
(D) 3/4
(E) 15/16

The OA is E.

I don't know how to solve this PS question. Experts, may you give me an explanation? I'd be thankful.

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Source: Beat The GMAT — Problem Solving | Sat Dec 23, 2017 3:37 am

elias.latour.apex: Master | Next Rank: 500 Posts; Posts: 228; Joined: Thu Apr 20, 2017 1:02 am; Location: Global; Thanked: 32 times; Followed by:3 members; GMAT Score:770

by elias.latour.apex » Mon Dec 25, 2017 1:45 pm

Well, one way to solve this problem is to figure his chance of tossing one heads, his chance of tossing two heads, his chance of tossing three heads, and his chance of tossing four heads and adding all those numbers up.

An easier way is to figure his chance of tossing all tails. If he doesn't toss all tails, then he must have tossed at least one heads.

The chance of tails four times is (1/2)^4 or 1/16 that he will toss nothing but tails.

Accordingly, he must have a 15/16 chance of tossing heads at least once.

Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Sep 05, 2019 5:17 am

M7MBA wrote:John flips a coin 4 times. What is the probability that he gets heads on at least one of the four flips?

(A) 1/16
(B) 1/4
(C) 1/2
(D) 3/4
(E) 15/16

The OA is E.

I don't know how to solve this PS question. Experts, may you give me an explanation? I'd be thankful.

We can use the formula:

P(at least one head on 4 flips) = 1 - P(no heads on 4 flips)

P(no heads on 4 flips) = (1/2)^4 = 1/16.

P(at least one head on 4 flips) = 1 - 1/16 = 15/16.

Answer: E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Sep 05, 2019 5:17 am

Scott@TargetTestPrep wrote:
M7MBA wrote:John flips a coin 4 times. What is the probability that he gets heads on at least one of the four flips?

(A) 1/16
(B) 1/4
(C) 1/2
(D) 3/4
(E) 15/16

We can create the equation:

(a^2) x (-3) = 3(3a + 2)

-a^2 = 3a + 2

-a^2 - 3a - 2 = 0

a^2 + 3a + 2 = 0

(a + 2)(a + 1) = 0

a = -2 or a = -1

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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