Question 952345: If Sam can get a grant to support her program, she feels that there is a .9 probability that the program will work. If she fails to get the grant, she feels that there will only be a .3 probability that it will be successful. If the probability of getting the grant is .6, what is the probability of success?
I have tried all kinds of distribution tables, and still cant seem to get it correct. PLEASE HELP. You dont have to give me the answer, just tell me what steps I need to figure it out.
Thanks :)
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Notation/Variable Setup:
G = gets a grant
W = program will work
P(G) = probability she gets the grant
P(G')= probability she doesn't get the grant
P(W|G) = probability program works IF she gets grant
P(W|G') = probability program works IF she does NOT get grant
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"what is the probability of success? " translation: "what is the probability of the program works, ie, what is P(W)? "
To compute P(W), we use the law of total probability, which in this specific case means: P(W) = P(W|G)*P(G) + P(W|G')*P(G')
So we need to find the following
P(W|G)
P(W|G')
P(G)
P(G')
So let's pick through the problem to pull out the needed info
"If Sam can get a grant to support her program, she feels that there is a .9 probability that the program will work", so P(W|G) = 0.9
"If she fails to get the grant, she feels that there will only be a .3 probability that it will be successful", so P(W|G') = 0.3
P(G) = 0.6 because "the probability of getting the grant is .6"
P(G') = 0.4 because 1-0.6 = 0.4
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Summary of what we're given
P(W|G) = 0.9
P(W|G') = 0.3
P(G) = 0.6
P(G') = 0.4
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Now we plug all this into the equation P(W) = P(W|G)*P(G) + P(W|G')*P(G') to get...
P(W) = P(W|G)*P(G) + P(W|G')*P(G')
P(W) = 0.9*0.6 + 0.3*0.4
P(W) = 0.54 + 0.12
P(W) = 0.66
The final answer is 0.66
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Jim
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Answer by edjones(8007)  (Show Source):
You can put this solution on YOUR website! .6*.9=.54 probability she gets the grant and is successful.
.4*.3=.12 probability she doesn't get the grant and is successful.
.54+.12=.66 probability she is successful.
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Ed
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