vaibhav101 wrote:2 marbles are drawn from a jar with 10 marbles. If all marbles are either red or blue, is the probability that both marbles selected will be red greater than 3/5?

1) the probability that both marbles selected will be blue is less than 1/10.
2) at least 60% of the marbles in the jar are red.

Say there are x Red marbles; thus, there are (10 - x) Blues marbles.

Probability of that both marbles selected will be red = xC2 / 10C2 = [x(x - 1)/1.2] / [10.9/1.2] = x(x - 1)/10.9

We have to determine whether x(x - 1)/10.9 > 3/5.

=>Question rephrased: Is x(x - 1) > 54?

Let's take each statement one by one.

1) the probability that both marbles selected will be blue is less than 1/10.

Probability that both marbles selected will be blue = (10 - x)C2 / 10C2 = [(10 - x)(9 - x)/1.2] / [10.9/1.2] = (10 - x)(9 - x)/10.9

=> (10 - x)(9 - x)/10.9 < 1/10

(10 - x)(9 - x) < 9

Since (10 - x) and (9 - x) are positive consecutive integers, the value of (10 - x)(9 - x) is either 3*2 (= 6) or 2*1 (= 2).

If (10 - x)(9 - x) = 3*2 => x = 7; and if (10 - x)(9 - x) = 2*1 => x = 8

Case 1: If x = 7

Is x(x - 1) > 54?

At x = 7, x(x - 1) > 54 = 7*6 = 42 < 54, the answer is No.

Case 2: If x = 8

Is x(x - 1) > 54?

At x = 7, x(x - 1) > 54 = 8*7 = 56 > 54, the answer is Yes.

No unique answer. Insufficient.

2) at least 60% of the marbles in the jar are red.[/quote]

x ≥ 6

We saw in Statement 1 that if x = 7 and 8, there is no unique answer, thus this statement is insufficient.

Even the combination of the two statements won't help. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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