Betty picks 4 random marbles from a bowl containing 3 white, 4 yellow, and 5 blue marbles.

The probability that exactly 1 of the 4 marbles drawn is blue is
_____ (I know that the probability is 5/12 and that simplifies to 0.4166 but that is not one of the answer choices) the answer choices are 0.0707, 0.2135, .3535, and .6465. Can you please help me solve this question I am really stuck and I have tried looking on other websites to no avail.

1 answer

There are 5 blue out of 12 marbles.

So, there is a 5/12 chance of drawing a blue marble. That means that in 4 draws, the chance of drawing a blue on the 1st draw only is

5/12 * 7/11 * 6/10 * 5/9 = 35/396

Now, add that to the chance of drawing a blue only on the 2nd, 3rd, of 4th draw and you get

4 * 35/396 = 35/99 = 0.3535