Mark is going to an awards dinner and wants to dress appropriately. He is running behind schedule and asks his little brother to randomly select an outfit for him. Mark has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie. All six of his possible outfits are listed below.
Let
A
AA be the event that Mark's little brother selects an outfit with a white shirt and grey slacks and
B
BB be the event that he selects an outfit with a black shirt.

A. AA = white dress shirt (1 out of 3 dress shirts), one pair of grey slacks (1 out of 2 slacks), any tie (1 option) = 1/3 * 1/2 = 1/6 probability, and 1 option (white dress shirt, grey slacks, and red tie)

B. BB = black dress shirt (1 out of 3 dress shirts), any slacks (2 options), any tie (1 option) = 1/3 probability, and 2 options (black dress shirt, grey slacks, red tie; black dress shirt, black slacks, red tie)

false

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80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !