A jar contains 8 red marbles and y white marbles. If Joan takes 2 random marbles from the jar, is it more likely that she will have 2 red marbles than that she will have one marble of each color?(1) y ≤ 8(2) y ≥ 4

Answer:a) y </= 8 is not sufficient b) y >/= 4 is sufficient (y is not less than 3.5)Step-by-step explanation:Number of Red marbles = 8Number of white marbles = yTotal number of marbles in the jar = 8+ yLet Pr(R) be the probability of picking red marbles Let Pr(W) be the probability picking white marbles Pr(R) = 8/ (8+y)Pr(W) = 7/(7+y)Pr(RR) = Pr(R1) * Pr( R2) = 8/(8+y) * 7/(7+y)Pr(RW) = Pr(R1) * Pr(W2) + Pr(W1) * Pr(R2)= 2[Pr(R1) * Pr(W2)= 2[8/(8+y) * y/(7+y)]The probability of having 2 red is greater than one marble of each color. Pr(RR) > Pr( RW) 8/(8+y) * 7/(7+y) > 2[8/(8+y) * y/(7+y)]7/(7+y) > 2(y/(7+y)7/y > 27/2 > y3.5 > yy < 3.5Therefore; a) y </= 8 is not sufficient b) y >/= 4 is sufficient (y is not less than 3.5)