At a carnival, the probability that a boy will win the 100 m event is

Question

At a carnival, the probability that a boy will win the 100 m event is 1/10, and the probability he wins the 200 m event is 1/8. If these events are independent, what is the probability that he wins only one of these events?

A. 1/80
B. 1/5
C. 17/80
D. 9/40
E. 4/5

A. 1/80
B. 1/5
C. 17/80
D. 9/40
E. 4/5

CrackverbalGMAT · Answer

P(Winning 100 m) = 1/10. Therefore P(Losing the 100m) = 1 - 1/10 = 9/10

P(Winning 200 m) = 1/8. Therefore P(Losing the 100m) = 1 - 1/8 = 7/8

P(Winning exactly 1 event) = Winning 100m and losing 200 m or Losing 100m and winning 200m

= (1/10 * 7/8) + (9/10 * 1/8) = 7/80 + 9/80 = 1680 = 1/5

Option B

Arun Kumar

TestPrepUnlimited · Answer

In order to win one event ONLY, he needs to win either one then lose the other one.

\frac{1}{10}*\frac{7}{8} + \frac{1}{8}*\frac{9}{10} = \frac{7 + 9}{80} = \frac{1}{5}

Ans: B

MathRevolution · Answer

P(100) =  \frac{1}{10}

P(not 100) =  \frac{9}{10}

P(200) =  \frac{1}{8}

P(not 200) =  \frac{7}{8}

Independent events: Only one: P(100) * P(not 200) + p(not 100) * P(200)

=>  \frac{1}{10} * \frac{7}{8} + \frac{9}{10} * \frac{1}{8}

=>  \frac{7}{80} + \frac{9}{80} 
 
=>  \frac{16}{80} = \frac{1}{5}

Answer B

dave13 · Answer

hi KarishmaB when we get 1/10 * 7/8= 7/80 why we dont result multiply by 2! I mean that 100m win and 200 m lose is one event and 200m lose and 100m win is another event same question applies to 1/8*9/10 For example in this question we consider different arrangements https://gmatclub.com/forum/there-are-10 ... l#p3203227

KarishmaB · Answer

Whether to multiply the probability by 2 or not (arrange or not) is one of the hardest things to explain.

I mean that  100m win and 200 m lose  is one event and  200m lose and 100m win  is another event

They are not two different cases. Whether you win the 100 m first or lose the 200 m first is irrelevant. The overall result is that you won the 100 m and lost the 200 m. That is the result. You ran the 100m when it was scheduled and ran the 200 m when it was scheduled. You did not choose the sequence and the sequence does not change the overall result. The sequence is pre-defined.

At a carnival, the probability that a boy will win the 100 m event is

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At a carnival, the probability that a boy will win the 100 m event is

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