There is a 30 % chance of rain and a 70% chance of shine. If

Question

There is a 30 % chance of rain and a 70% chance of shine. If it rains there is a 50% chance that Bob will cancel his picnic but if the sun is shining he will definitely have his picnic. What is the chance that Bob will have his picnic?

A. 0.15
B. 0.25
C. 0.75
D. 0.85
E. 0.9

Show Answer

Official Answer

D

A. 0.15
B. 0.25
C. 0.75
D. 0.85
E. 0.9

KarishmaB · Accepted Answer

To figure out whether you need OR/AND, focus on how you speak about it.
You say, "I need a shirt AND a trouser" - AND so multiplication
"I need a shirt OR a T-shirt" - OR so addition

Here you say: It will Rain OR Shine
Rains - probability of party is 15%
Shines - probability of party is 70%

Since it will Rain OR Shine, total probability = 15% + 70% = 85%

Bunuel · Answer

50% chance that Bob will cancel his picnic in case of a rain means that there is 50% chance that Bob will NOT cancel his picnic in case of a rain. So,  P=0.3*0.5+0.7*1=0.85 .

Answer: 0.85.

Or  P(picnic)=1-P(no \ picnic)=1-0.3*0.5=0.85 .

Answer: 0.85.

ajit257 · Answer

why are we adding .7..how do I figure out whether it is OR/AND solution to see if it has to be added or multiplied

Bunuel · Answer

Bob will have his picnic in two cases:
I. there is no rain and he goes: 0.7*1;
II. there is a rain and he still goes: 0.3*0.5;

So you should add the individual probabilities of these events.

Bunuel · Answer

You can directly translate the question into probability:

Bob will have his picnic if: there is no rain (0.7) AND he goes (1) OR there is a rain (0.3) AND he still goes (0.5).

Now, put * for AND and + for OR: 0.7*1+0.3*0.5.

144144 · Answer

650??? rly? thats an ez one no?

do u have one of this kind that will be harder to solve? is this kind of question is common?

thanks.

KarishmaB · Answer

Actually, P & C questions, though easy if understood well, are considered a little harder.... You will not see more than 1 or 2 questions from this topic generally... It is always a good idea to have your basics clear so that you can tackle the easier questions on this topic... they would still be higher on the scoring scale...

BrentGMATPrepNow · Answer

P(picnic takes place) = P(sunshine   AND   the picnic takes place given that we have sunshine   OR    it rains   AND   the picnic takes place) 
=   x   P(the picnic takes place given that there was sunshine)]    +      x   P(the picnic takes place given that it rained)] 
=   x   1]    +      x   0.5]
= 0.7 + 0.15
= 0.85 
= 85%

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There is a 30 % chance of rain and a 70% chance of shine. If

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