BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

On his drive to work, Leo listens to one of three radio

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

On his drive to work, Leo listens to one of three radio

by BTGmoderatorLU » Thu Aug 16, 2018 3:17 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Source: GMAT Prep

On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?

A. 0.027
B. 0.090
C. 0.417
D. 0.657
E. 0.900

The OA is D.
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sat Aug 18, 2018 6:16 pm
Hi All,

We're told that Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. We're asked for the probability that Leo will hear a song he likes. While this question is a bit wordy, it's based on standard Probability rules.

With Probability questions, there are two outcomes that you can calculate: what you WANT to happen and what you DON'T want to happen. Since the sum of those two fractions is always 1, sometimes the easiest way to calculate what you WANT to happen is to calculate what you DON'T want and then subtract that fraction from 1.

This question asks for the probability that Leo will hear a song that he likes among 3 options. Instead of calculating all of the different ways for that to occur, we'll calculate the probability that he does NOT hear a song that he likes on any of the stations...

Probability of hearing a song that he likes = .3
Probability of NOT hearing a song that he likes = 1 - .3 = .7

Probability of NOT hearing a song that he likes on ALL 3 stations = (.7)(.7)(.7) = (.7)(.49) = .343

Thus, the probability that he will hear a song that he likes is 1 - .343 = .657

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Mon Aug 20, 2018 10:47 am
BTGmoderatorLU wrote:Source: GMAT Prep

On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?

A. 0.027
B. 0.090
C. 0.417
D. 0.657
E. 0.900

The probability that Leo will hear a song he likes on the way to work is the probability he will not turn off his radio. That is, either station A will be on for the entire trip, or station B or C will be on by the end of the trip.

The probability that station A will be on for the entire trip is 0.3.

Station B will be on by the end of the trip if station A did not play a song he likes AND station B did play a song he likes. The probability is 0.7 x 0.3 = 0.21.

Station C will be on by the end of the trip if station A did not play a song he likes AND station B did not play a song he likes AND station C did play a song he likes. The probability is 0.7 x 0.7 x 0.3 = 0.147.

Since these events are mutually exclusive, we add their probabilities, so the probability that a station will be on by the end of the trip is 0.3 + 0.21 + 0.147 = 0.657.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1