On Monday morning, Chris receives tickets to a baseball

Question

On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 40% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?

(A) 36%
(B) 60%
(C) 66%
(D) 80%
(E) 84%

(A) 36%
(B) 60%
(C) 66%
(D) 80%
(E) 84%

Bunuel · Answer

Chris won't be able to attend the game if it be raining on Monday evening  and  Tuesday evening. The probability of that is 0.4*0.4 = 0.16. So, the probability that he will be able to attend is 1 - 0.16 = 0.84.

Answer: E.

bhatiavai · Answer

does it really matter whether it rains of Tuesday or not ?

The question states that chris is flying out on the morning of Wednesday and the match takes place at 7PM...

Am I missing something here ?

KarishmaB · Answer

He gets the tickets on Monday morning. 
"Next evening that does not rain" includes Monday evening too. So next two evenings means Monday evening and Tuesday evening.

aviram · Answer

This is more of an English question than math :D

b2bt · Answer

I still don't get it. Does the question means that he gets to see the game only if it doesn't rain at all? On monday and on tuesday too?

OE by Veritas Prep  
E. Two sequences work for Chris to attend the game: Either it doesn't rain on Monday night (60% chance) or it does rain on Monday night but then not on Tuesday night (a 40% chance that it doesn't rain Monday, then a 60% chance it doesn't rain Tuesday). The first probability is 3/5, and the second is (2/5)(3/5) = 6/25. Converting to find a common denominator, that's 15/25 + 6/25 = 21/25, which converts to 84%.

Alternatively, you could look at it by seeing that  the only way he cannot see the game  is that it rains both nights, a 40% * 40% = 16% sequence. If 16% of the outcomes don't work for him, then 84% do, again making the answer E.

What if it doesn't rain on Monday but rains on Tuesday?

LaxAvenger · Answer

I calculated this way:

Monday : No rain: 0,6 OR
Tuesday: Rain on Monday (0,4) AND No rain on Tuesday (0,6) --> 0,4*0,6

= 0,6 + 0,24 = 0,84

Answer E

KarishmaB · Answer

The question says, "...Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain"

So if it does not rain on Monday evening, the game will be played on Monday evening and will be over. After that, what happens on Tuesday is immaterial. The probability of no rain on Monday is 3/5.

If it does rain on Monday, the game will not be played on Monday. This probability is 2/5. Then if it does not rain on Tuesday evening, the game will take place on Tuesday evening. Hence probability of game on Tuesday evening is (2/5)*(3/5).

In these two cases, Chris will see the game. Total Probability = 3/5 + (2/5)*(3/5) = .84

If it rains on Tuesday too, then the game will be shifted by another day. In that case, Chris will not be able to see the game since he will fly out on Wednesday morning.

b2bt · Answer

Oh so by next evening it meant the evening of the same day itself (Chris got the tickets on Monday itself). For some reasons, I thought 'next evening' meant Tuesday evening.
Thanks Karishma

mvictor · Answer

i'm sure the answers above are good enough, but here is how I solved:
we have only 2 days when he can attend.
both days have 40% chance of raining. 
thus, the overall probability that he will attend the game is: either on 1st day (0.6) or on the second day (0.4-probability that it will rain on monday *0.6 - probability that it will not rain on tuesday)

thus, 0.6+0.24 = 0.84, or 84%.
E

MohidSayed · Answer

Hi Bunuel,

In the question, by ‘next evening’ I assumed it meant that the game is not happening this evening that is on Monday evening. Am I wrong in understanding?

Posted from my mobile device

YASH750 · Answer

The question says , if it doesnt rain the match is played that evening . If it rains , the match is played the following evening (next day). 
so we know the person is in town only till wednesday morning .

so we have two evenings in this case .
monday evening and tuesday evening.

Probablity of game on a monday is 0.6

probablity of game on tuesday follows the following logic.: it rains on monday evening AND doesnt rain on tuesday evening.
 =0.4*0.6=0.24

so adding the two probablities we get 06.+0.24=0.84=84%

kayarat600 · Answer

Next evening always implies some other day because we already have an evening today.

On Monday morning, Chris receives tickets to a baseball

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On Monday morning, Chris receives tickets to a baseball

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