Cameron has a bag with 10 white marbles and 15 black marbles. What is the probability...

Cameron has a bag with 10 white marbles and 15 black marbles. What is the probability that he will choose (on two separate draws) two white marbles without replacement.

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Expert Solution

It is given that Cameron has a bag with 10 white marbles and 15 black marbles. We have to find the probability that he will choose (on two separate draws) two white marbles without replacement.

Total number of marbles = 10 + 15 = 25

Case 1 : When the first marble is white. There are 10 white marbles. So, we can choose 1 white marble from these 10 white marbles in 101 ways. Thus, the probability that the first marble is white = 10/25.

Case 2 : When the second marble is also white. As the marbles are chosen without replacement, thus, after choosing the first white marble, we are left with 9 white marbles. After choosing the first marble, so, we are left with 24(25-1=24) marbles. Thus, the probability that the second marble is also white = 9/24.

Thus, the required probability = (10/25)*(9/24) = (10*9)/(25*24) = 90/600 = 0.15 .

Thus, the probability that he will choose (on two separate draws) two white marbles without replacement = 0.15 .

orchestra answered 1 year ago

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