1. If the joint probability is given by:x+yf(x, y) =30for r = 0, 1, 2, 3; y = 0, 1, 2,Find:(a) P(X < 2, Y = 1);(b) P(X > 2, Y<1);(c) P(X>Y );(d) P(X + Y = 4). 2. From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in thesample, find:(a) the joint probability distribution of X and Y;(b) P[(X, Y ) E A], where A is the region that is given by {(x, y) | x + y < 2}.

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A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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If the joint probability is given by:f(x,y) = (2x + 2y)/40, for x = 0, 1, 2, 3; y = 0, 1, 2, 3 a.) Find P(X>Y ): b.) Find P(X > 2, Y ≤ 1): c.) Is the equation valid? YES OR NO d.) Find P(X ≤ 2, Y = 1): e.) Find P(X + Y = 4):

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1. If the joint probability is given by: x+ y f(r, y) = 30 for r = 0, 1, 2, 3; y = 0, 1, 2, Find: (a) P(X < 2, Y = 1); (b) P(X > 2, Y < 1); (c) P(X>Y ); (d) P(X + Y = 4).