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# If the probability that Brendon, Daniel and Kane score more than or eq

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Math Expert
Joined: 02 Sep 2009
Posts: 65831
If the probability that Brendon, Daniel and Kane score more than or eq  [#permalink]

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02 Jun 2020, 06:56
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Difficulty:

45% (medium)

Question Stats:

61% (02:09) correct 39% (02:28) wrong based on 33 sessions

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If the probability that Brendon, Daniel and Kane score more than or equal to 700 on the GMAT is 0.4, 0.5 and 0.6 respectively, what is the probability that at least 2 of them score less than 700?

A. 0.12
B. 0.38
C. 0.40
D. 0.50
E. 0.60

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Re: If the probability that Brendon, Daniel and Kane score more than or eq  [#permalink]

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02 Jun 2020, 07:45
Bunuel wrote:
If the probability that Brendon, Daniel and Kane score more than or equal to 700 on the GMAT is 0.4, 0.5 and 0.6 respectively, what is the probability that at least 2 of them score less than 700?

A. 0.12
B. 0.38
C. 0.40
D. 0.50
E. 0.60

getting >700 ; .4,.5,.6
and <700 ; .6,.5,.4
we get 4 cases considering atleast 2 get <700 score
.4*.5*.4+.5*.6*.4+.6*.6*.5+.6*.5*.4
=> .08+.12+.18+.12
=> 0.5
OPTION D
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Re: If the probability that Brendon, Daniel and Kane score more than or eq  [#permalink]

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02 Jun 2020, 23:56
Bunuel wrote:
If the probability that Brendon, Daniel and Kane score more than or equal to 700 on the GMAT is 0.4, 0.5 and 0.6 respectively, what is the probability that at least 2 of them score less than 700?

A. 0.12
B. 0.38
C. 0.40
D. 0.50
E. 0.60

Solution

• P(at least 2 of them score less than 700) = P( Exactly 2 of them score less than 700) + P(All three score less than 700)

• Probability that Brendon scores less than 700 $$= 1-0.4 = 0.6$$
• Probability that Daniel scores less than 700 $$= 1-0.5 = 0.5$$
• Probability that Kane scores less than 700 $$= 1-0.6 = 0.4$$

• P(All three score less than 700) $$= 0.6*0.5*0.4$$
• P( Exactly 2 of them score less than 700) $$= 0.4*0.5*0.4 + 0.6*0.5*0.4 +0.6*0.5*0.6$$
• Thus, P(at least 2 of them score less than 700) $$=0.6*0.5*0.4 + 0.4*0.5*0.4 + 0.6*0.5*0.4 +0.6*0.5*0.6= 0.5$$
Thus, the correct answer Option D.
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Re: If the probability that Brendon, Daniel and Kane score more than or eq   [#permalink] 02 Jun 2020, 23:56