From a sack of fruit containing 3 apples, 3 oranges, and 3 bananas, a random sample of4 pieces of fruit is selected. Suppose X is the number of apples and Y is the number oforanges 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 + y ≤3}.(a) Complete the joint probability distribution below.(Type integers or simplified fractions.)f(x,y)y 0123400-|- -|142114142011423143141420X211431411400(b) The probability is(Type an integer or a simplified fraction.)3142142000400000 A coin is tossed twice. Let Z denote the number of heads on the first toss and W thetotal number of heads on the 2 tosses. Suppose the coin is unbalanced and a head hasa 64% chance of occurring. Complete parts (a) through (d).(a) Find the joint probability distribution of W and Z.Select the correct choice below and fill in the answer boxes to complete your choice.(Type integers or decimals. Do not round.)A.B.ZB.Zf(w,z)0f(w,z)0Wg(w)2Wg(w)00.129600W10.23040.2304(b) Find the marginal distribution of W.Select the correct choice below and fill in the answer boxes to complete your choice.(Type integers or decimals. Do not round.)A.011W120.409622

Since you have posted multiple questions, we will provide the solution only to the first questions…

From a sack of fruit containing 3 apples, 3 oranges, and 3 bananas, a random sample of 4 pieces of fruit is selected. Suppose X is the number of apples and Y is the number of oranges 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 + y ≤3}. (a) Complete the joint probability distribution below. (Type integers or simplified fractions.) y f(x,y) 1 2 3 4 0 0 1 _2 1]4 1]20 42 42 1 1 0|- |~ |w5| 42 X 2 1 14 3 14 1 14 0 0 (b) The probability is (Type an integer or a simplified fraction.) 3 1 42 1 42 0 0 4 0 0 0 0 0