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 = 8
Number of white marbles = y
Total number of marbles in the jar = 8+ y
Let 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 > 2
7/2 > y
3.5 > y
y < 3.5
Therefore;
a) y </= 8 is not sufficient
b) y >/= 4 is sufficient (y is not less than 3.5)
