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

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Manager
Joined: 28 Aug 2010
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There is a 30 % chance of rain and a 70% chance of shine. If  [#permalink]

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22 Jan 2011, 08:21
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64% (00:34) correct 36% (00:16) wrong based on 41 sessions

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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?
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Updated on: 23 Jan 2011, 04:37
If you har having trouble with probabilities I'd recommend drawing probability tree.

In this case we just multiply .3 * .5 and adds .7 = 85%

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Originally posted by Mackieman on 22 Jan 2011, 08:29.
Last edited by Mackieman on 23 Jan 2011, 04:37, edited 1 time in total.
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There is a 30 % chance of rain and a 70% chance of shine. If  [#permalink]

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22 Jan 2011, 08:43
ajit257 wrote:
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?

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, $$P=0.3*0.5+0.7*1=0.85$$.

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

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22 Jan 2011, 10:19
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
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22 Jan 2011, 10:26
ajit257 wrote:
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

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.
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25 Jan 2011, 07:32
Bunuel wrote:
ajit257 wrote:
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

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.

Just adding another way of arriving at the same result.
Because there are only two outcomes, we can calculate the probability for no picnic and subtract it from 1 to get the probability for picnic

probability for no picnic = 0.3 * 0.5 = 0.15
so probability of picnic is = 1 - 0.15 = 0.85
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03 Feb 2011, 01:19
Chance of no picnic+chance of picnic= 100% ... (i)
Chance of picnic=100%-Chance of no picnic ... (ii)

Chance of no picnic= 50% of 30%= 15%

Therefore, According to (ii), Chance of picnic= 100%-15%= 85%. Answer.
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03 Feb 2011, 12:33
2
ajit257 wrote:
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

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%
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03 Feb 2011, 13:03
1
VeritasPrepKarishma wrote:
ajit257 wrote:
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

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%

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.
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04 Feb 2011, 04:45
Rain: 3/10; 1/2 chance.
Shine: 7/10; 1

$$\frac{3}{10}*\frac{1}{2}+\frac{7}{10}*\frac{1}{1}$$
$$\frac{17}{20}$$
$$85\%$$
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05 Feb 2011, 07:52
what lvl is that question?
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06 Feb 2011, 13:05
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.
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06 Feb 2011, 19:43
144144 wrote:
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.

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... Veritas Permutation book is full of examples of these kind of questions. I will put up a couple on this topic from the book soon....
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Karishma
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06 Feb 2011, 21:02
thanks VeritasPrepKarishma
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Re: There is a 30 % chance of rain and a 70% chance of shine. If  [#permalink]

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06 Oct 2018, 02:25
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Re: There is a 30 % chance of rain and a 70% chance of shine. If   [#permalink] 06 Oct 2018, 02:25
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