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A series of baseball games is scheduled to be played on Friday and Sat

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A series of baseball games is scheduled to be played on Friday and Sat  [#permalink]

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New post 13 Apr 2018, 03:02
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A
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E

Difficulty:

  55% (hard)

Question Stats:

23% (00:39) correct 77% (00:57) wrong based on 43 sessions

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A series of baseball games is scheduled to be played on Friday and Saturday. If it rains on either day, the game scheduled for that day will be cancelled. If there is a 50% chance of rain on Friday and a 70% chance of rain on Saturday, what is the probability that the game will be cancelled on one of the two days?

A. 20%
B. 35%
C. 50%
D. 75%
E. 85%

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Re: A series of baseball games is scheduled to be played on Friday and Sat  [#permalink]

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New post 13 Apr 2018, 05:01
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Bunuel wrote:
A series of baseball games is scheduled to be played on Friday and Saturday. If it rains on either day, the game scheduled for that day will be cancelled. If there is a 50% chance of rain on Friday and a 70% chance of rain on Saturday, what is the probability that the game will be cancelled on one of the two days?

A. 20%
B. 35%
C. 50%
D. 75%
E. 85%



The probability that the game will be cancelled on both days is 50% * 70% = 35%

The probability that the game will be played on both days is (100%-50%) * (100% -70%) = 50% * 30% = 15%

The probability that the game will be cancelled on one of the two days is 100% - (probability cancelled on both days+ Probability played on both days)

= 100 -(35%+15%) = 100 -50% = 50%

Hence option C = 50% is the answer.

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Re: A series of baseball games is scheduled to be played on Friday and Sat  [#permalink]

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New post 13 Apr 2018, 12:25
Simply we can solve this..

Proba.of game played in friday * probab.of game not played in saturday + probabi.of game not played in friday * prob.of game played in saturday.
So
50/100*70/100 + 50/100*30/100 = 1/2 = 50%

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Re: A series of baseball games is scheduled to be played on Friday and Sat  [#permalink]

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New post 13 Apr 2018, 13:21
Bunuel wrote:
on Friday and Saturday...what is the probability that the game will be cancelled on one of the two days?


I'm confused, since there is no condition such as "exactly on one of two days". I understand this problem as "cancelled on any of 2 days (including both)"

P(1)+P(2)+P(both) = 85%. Answer (E)

Please, help me out if I'm wrong.
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Re: A series of baseball games is scheduled to be played on Friday and Sat  [#permalink]

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New post 15 Apr 2018, 01:18
Hero8888 wrote:
Bunuel wrote:
on Friday and Saturday...what is the probability that the game will be cancelled on one of the two days?


I'm confused, since there is no condition such as "exactly on one of two days". I understand this problem as "cancelled on any of 2 days (including both)"

P(1)+P(2)+P(both) = 85%. Answer (E)

Please, help me out if I'm wrong.


Since it is mentioned on one of the 2 days. It means exactly one day.
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Re: A series of baseball games is scheduled to be played on Friday and Sat  [#permalink]

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New post 16 Apr 2018, 17:08
Bunuel wrote:
A series of baseball games is scheduled to be played on Friday and Saturday. If it rains on either day, the game scheduled for that day will be cancelled. If there is a 50% chance of rain on Friday and a 70% chance of rain on Saturday, what is the probability that the game will be cancelled on one of the two days?

A. 20%
B. 35%
C. 50%
D. 75%
E. 85%


We can use the equation:

1 = P(will be canceled on one of the two days) + P(will be cancelled on both days) + P(will not be cancelled on either day)

We have:

P( will not be canceled on either day) = P(will be played on both days) = 0.5 x 0.3 = 0.15

P(will be cancelled on both days) = 0.5 x 0.7 = 0.35

Thus,

P(will be cancelled on one of the two days) = 1 - 0.15 - 0.35 = 0.5

Answer: C
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Re: A series of baseball games is scheduled to be played on Friday and Sat &nbs [#permalink] 16 Apr 2018, 17:08
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