Probability

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

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

vaibhav101: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon May 01, 2017 11:56 pm; Thanked: 4 times

Probability

by vaibhav101 » Sat Jun 16, 2018 1:26 am

Timer

00:00

Your Answer

Global Stats

a box contains 2 tennis, 3 cricket and 4 squash balls. 3 balls are drawn in succession with replacement. Find the probability that all 3 are of same type.

A 12/81
B 1/9
C 18/81
D 11/81
E none of these

Quote

Source: Beat The GMAT — Problem Solving | Sat Jun 16, 2018 1:26 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Jun 16, 2018 4:34 am

vaibhav101 wrote:a box contains 2 tennis, 3 cricket and 4 squash balls. 3 balls are drawn in succession with replacement. Find the probability that all 3 are of same type.

A 12/81
B 1/9
C 18/81
D 11/81
E none of these

P(all 3 are same type) = P(all 3 are tennis OR all 3 are cricket OR all 3 are squash)
= P(all 3 are tennis) + P(all 3 are cricket) + P(all 3 are squash)
= P(1st is tennis AND 2nd is tennis AND 3rd is tennis) + (1st is cricket AND 2nd is cricket AND 3rd is cricket) + P(1st is squash AND 2nd is squash AND 3rd is squash)
= [2/9 x 2/9 x 2/9] + [3/9 x 3/9 x 3/9] + [4/9 x 4/9 x 4/9]
= 8/9Â³ + 27/9Â³ + 64/9Â³
= 99/9Â³
= 11/9Â²
= 11/81

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon May 06, 2019 7:14 pm

vaibhav101 wrote:a box contains 2 tennis, 3 cricket and 4 squash balls. 3 balls are drawn in succession with replacement. Find the probability that all 3 are of same type.

A 12/81
B 1/9
C 18/81
D 11/81
E none of these

The probability they are all tennis balls is 2/9 x 2/9 x 2/9 = 8/729.

The probability they are all cricket balls is 3/9 x 3/9 x 3/9 = 27/729.

The probability they are all squash balls is 4/9 x 4/9 x 4/9 = 64/729.

Therefore, the probability the 3 balls are of the same type is 8/729 + 27/729 + 64/729 = 99/729 = 11/81.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]