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From a sack of fruit containing 3 bananas, 2 apples, and 2 oranges, a random sample of 4 pieces of fruit is selected. Suppose X is the number of bananas and Y is the number of apples in the sample. (a) Find the joint probability distribution of X and Y. (b) Find P[(X, Y)EA], where A is the region that is given by {(x,y) | x + ys 2}. (a) Complete the joint probability distribution below. (Type integers or simplified fractions.) NX f (x,y) 0 3 4 y C W N - (b) The probability is (Type an integer or a simplified fraction.)A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is as shown below. Complete parts (a) through (c). 2 05 51,05 51 f(x,y)= 11 (3x+8y)i x y 0, elsewhere (a) Find the marginal density of X. Select the correct choice below and ll in the answer box to complete your choice. 0 A. g(x)=|:,forosxs1 Q 3_ h(y)=|:,forosys1 (b) Find the marginal density of Y. Select the correct choice below and ll in the answer box to complete your choice. 0 A. g(x)=|:,forosxs1 O 3_ h(y)=|:,for05ys1 (c) Find the probability that the drive-through facility is busy less than one-third of the time. The probability is E. (Type an integer or a simplied fraction.)