The probability of the blue (question A) is going to be 0.3535 (C).
The probability of the white (question B) is going to be 0.7455 (D). -> the probability (that none are white) = (9/12)(8/11)(7/10)(6/9) which = 14/55 the probability (that at least one of them are white) = 1- 14/55 which = 41/55 which makes your answer .7455 (this is the example of the white so you can see how I got the answer)
Lisa has a great explanation for part B already, so I'll only focus on part A
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We have 3 white, 4 yellow and 5 blue. So there are 3+4+5 = 12 marbles total
The probability of picking blue for the first selection is 5/12
The next selection has the probability of 7/11 because there are 7 non-blue marbles (3 white+4 yellow) out of 12-1 = 11 left over
The next selection after that is going to have a probability of 6/10. Simply subtract 1 from the numerator and denominator
Similarly, we go from 6/10 to 5/9
So if we wanted to know the probability of getting blue in slot 1, and non-blue everywhere else, then we multiply out the fractions (5/12)*(7/11)*(6/10)*(5/9) = 0.08838
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We have 4 cases Case 1) Blue is in slot 1, non-blue everywhere else Case 2) Blue is in slot 2, non-blue everywhere else Case 3) Blue is in slot 3, non-blue everywhere else Case 4) Blue is in slot 4, non-blue everywhere else
when we calculated 0.08838 earlier, we found the probability for case (1) to happen. We want to account for all four cases. Simply multiply 0.08838 by 4 to do this 4*0.08838 = 0.35352 which rounds to 0.3535
