SOLUTION: A box contains two black balls and three gold balls. Two balls are randomly drawn in succession from the box. a. If there is no replacement, what is the probability that both ba

Question 200336: A box contains two black balls and three gold balls. Two balls are randomly drawn in succession from the box.
a. If there is no replacement, what is the probability that both balls are black? I thought it would be 2/5 + 1/4 = 9/20 or .45 I was not sure if this was the correct answer.
b. If there is replacement before the second draw, what is the probability that both balls are black?
I thought it would be 2/5 + 2/5 = 4/5 or .80 but I was not sure if this was the correct answer
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You're confusing "and" and "or". With "and", you multiply the probabilities.

a)

P(Black AND Black) = P(Black) * P(Black)

P(Black AND Black) = (2/5) * (1/4)

P(Black AND Black) = 2/20

P(Black AND Black) = 1/10

P(Black AND Black) = 0.1 which is 10%

So there's a 10% chance that you select both black balls (without replacement)

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b)

P(Black AND Black) = P(Black) * P(Black)

P(Black AND Black) = (2/5) * (2/5)

P(Black AND Black) = 4/25

P(Black AND Black) = 0.16 which is 16%

So there's a 16% chance that you select both black balls (with replacement)

If you aren't sure about the answers, you can use a smaller sample and draw a tree to display all the possible outcomes (this will help you calculate the probabilities)
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