Question 1001039: These are Conditional Probability questions of events involving "AND" and I'm having trouble understanding how to solve them. So If someone kindly could show and explain why then I would be so happy :) Thank You.
A pet store has seven puppies, including four poodles, two terriers, and one retriever. If Rebecka and Aaron, in that order, each select one puppy at random, with replacement ( they may both select the same one), find the probability of each event.
14) Rebecka selects a retriever, Aaron selects a terrier
16) both select a retriever
So...the next one is a follow up question with the same dogs
Suppose two puppies are selected as earlier, but this time without replacement (Rebecka and Aaron cannot both select the same puppy). Find the probability of each event.
17) both select a poodle
18) Aaron selects a terrier, given Rebecka selects a poodle
19) Aaron selects a retriever, given Rebecka selects a poodle
20) Rebecka selects a retriever
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A pet store has seven puppies, including four poodles, two terriers, and one retriever.
If Rebecka and Aaron, in that order, each select one puppy at random, with replacement ( they may both select the same one), find the probability of each event.
14) Rebecka selects a retriever AND Aaron selects a terrier
Ans:P(retriever AND terrier) = P(retriever)*P(terrier) = (1/7)(2/7) = 1/7
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16) both select a retriever
Ans: P(retriever AND retriever) = [P(retriever)]^2 = (1/7)^2 = 1/14
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So...the next one is a follow up question with the same dogs
Suppose two puppies are selected as earlier, but this time without replacement (Rebecka and Aaron cannot both select the same puppy). Find the probability of each event.
[A pet store has seven puppies, including four poodles,
two terriers, and one retriever.]
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17) both select a poodle
P(poodle AND poodle) = (4/7)(3/6) = 12/42 = 6/21 = 2/7
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18) Aaron selects a terrier, given Rebecka selects a poodle
P(terrier | poodle) = (2/6)(4/7) = 4/21
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19) Aaron selects a retriever, given Rebecka selects a poodle
P(retriever |poodle) = (1/6)(4/7) = 2/21
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20) Rebecka selects a retriever
Ans: 1/7
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Cheers,
Stan H.
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