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An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what

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An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what

by Gmat_mission » Thu Jul 02, 2020 1:51 am

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An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability that the sum of the 2 numbers on the balls will be even?

A. 25%
B. 37.5%
C. 50%
D. 62.5%
E. 75%

[spoiler]OA=C[/spoiler]

Source: Veritas Prep
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Re: An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, wh

by Brent@GMATPrepNow » Thu Jul 02, 2020 4:53 am
Gmat_mission wrote: ↑
Thu Jul 02, 2020 1:51 am
 An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability that the sum of the 2 numbers on the balls will be even?

A. 25%
B. 37.5%
C. 50%
D. 62.5%
E. 75%

[spoiler]OA=C[/spoiler]

Source: Veritas Prep
There are 2 possible ways to get an EVEN sum:
1) The 1st and 2nd balls are both EVEN
2) The 1st and 2nd balls are both ODD

So, P(sum is even) = P(1st is even AND 2nd is even OR 1st is odd AND 2nd is odd)
= P(1st is even AND 2nd is even) + P(1st is odd AND 2nd is odd)
= [P(1st is even) x P(2nd is even)] + [P(1st is odd) x P(2nd is odd)]
= [1/2 x 1/2] + [1/2 x 1/2]
= 1/4 + 1/4
= 1/2
= 0.5
= 50%

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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