Probability Question from Strategy Guide 5 - pg65 #5

[skyjarrett12]

A magician has 5 animals:3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he wil have a matched pair?

ANS. 4/10=40%

I'm trying to understand why my approach is incorrect. I did:
P(Both doves)=3/5 x 3/5
P(Both rabbits)= 2/5 x 2/5
Therefore, Probability of both doves OR both rabbits=
(3/5 x 3/5) + (2/5 x 2/5) = 13/25

Why is this not correct?

[kyle_proctor]

Have to test two possible scenarios: Either the magician pulls two doves in a row OR the magician pulls two rabbits in a row.

Start with the probability of pulling two doves:

5 total animals in pool -----> 3 of which are doves

(3/5) - probability of pulling a dove on the first pull.

(2/4) - probability of pulling a dove on the second pull. Here we assume the first pull was a dove, which is why we only have two doves left to select from the pool of 4 (remember we pulled one out of the pool).

(3/5) x (2/4) = 3/10


Probability of pulling two rabbits:

(2/5) - probability of pulling one rabbit

(1/4) - probability of pulling another rabbit (Here again we assume we pulled a rabbit on the first draw, which leaves one rabbit left in the pool)

(2/5) x (1/4) = 1/10



Now: These are the two possible scenarios for pulling two consecutive animals from the pool. Therefore, we must add their probabilities.

3/10 + 1/10 = 4/10

Hope that helps.

[skyjarrett12]

Kyle_proctor -

This is so helpful and SO much simpler than the explanation in the Strategy Guide!

Thanks so much!

[tim]

Thanks Kyle..