In a laundery bin, there are 33 socks. 21 are crew cut socks, and the rest are l

Question

In a laundery bin, there are 33 socks. 21 are crew cut socks, and the rest are low-cut socks. Of the crew cut, there are 12 black, 7 white, and 2 gray. Of the low-cut socks, there are 5 black, 4 white, and 3 gray.

a. If two socks are randomly selected, without replacement, what's the probability that the first sock is a crew sock and second is either white or gray?

b. If a dice is tossed, when a 1 or 6 is rolled, two socks will be drawn without replacement, if neither a 1 or 6 are rolled, three socks will be drawn without replacement. What is the probability, among the drawn socks, there will be at least one white sock?

Explanation / Answer

1) Probaibltiy = Non-white or gray crew sock , White or gray sock + White or gray crew sock , White or gray sock

=12/33 * 16/32 + 9/33*15/32 = (192+135)/(33*32) = 0.3096

B) Probability = 1-P(No white sock) = 1 - [2/6 *( 22C2/33C2) + 4/6* (22C3/33C3) ] = [ 1 - 4/6*0.2822 - 0.14588] = 0.6659

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