Question

4. From a bag having 7 mangoes and 3 apples, I draw 4 fruits WITHOUT replacement. Let X be the number of mangoes I get. What is the range of X? What is the distribution?

5. From a bag having 7 mangoes and 3 apples, I take out a fruit at random one at a time WITHOUT replacement until I get a mango. What is the probability distribution? Can you

find the expectation?

Answer 1

4. Given the bag contain 7 mangoes and 3 apples i.e., total of 10 and I draw 4 fruits without replacement. If X represents the number of mangoes, then the range of X = {1,2,3,4}

P(X=1) = P(1 mango, 3 apples) = (7C1*3C3)/10C4 = 7/210 = 0.033

P(X=2) = P(2 mango, 2 apples) = (7C2*3C2)/10C4 = (21*3)/210 = 63/210 = 0.3

P(X=3) = P(3 mango, 1 apples) = (7C3*3C1)/10C4 = (35*3)/210 = 105/210 = 0.5

P(X=4) = P(4 mango, 0 apples) = (7C4*3C0)/10C4 = (35*1)/210 = 35/210 = 0.167

We solve only one question in one post. Please post again for the solution of 5th question.