In a bowl of marbles, 8 are yellow, 6 are blue, and 4 are black. If Michelle picks 2 marbles out of the bowl at random a

[BTGmoderatorDC]

In a bowl of marbles, 8 are yellow, 6 are blue, and 4 are black. If Michelle picks 2 marbles out of the bowl at random and at the same time, what is the probability that at least one of the marbles will be yellow?

(A) 5/17

(B) 12/17

(C) 25/81

(D) 56/81

(E) 4/9


OA B

Source: Veritas Prep

[swerve]

In a bowl of marbles, 8 are yellow, 6 are blue, and 4 are black. If Michelle picks 2 marbles out of the bowl at random and at the same time, what is the probability that at least one of the marbles will be yellow?

(A) 5/17

(B) 12/17

(C) 25/81

(D) 56/81

(E) 4/9


OA B

Source: Veritas Prep

There is a total of 18 marbles.

It's more easier to start with the probability to pick none of the yellow marbles \(\Rightarrow \dfrac{10}{18} \cdot \dfrac{9}{17} = \dfrac{5}{17}\)

The probability to pick up at least one yellow marble (\(1-\) the probability to have none) will be
\(1 - \dfrac{5}{17} = \dfrac{12}{17} \Rightarrow\) B

[Scott@TargetTestPrep]

In a bowl of marbles, 8 are yellow, 6 are blue, and 4 are black. If Michelle picks 2 marbles out of the bowl at random and at the same time, what is the probability that at least one of the marbles will be yellow?

(A) 5/17

(B) 12/17

(C) 25/81

(D) 56/81

(E) 4/9


OA B

Solution:

We can look at this problem in terms of only 2 possible events. Either at least 1 yellow marble will be selected or no yellow marbles will be selected (but instead blue and black marbles will be selected). This means that

P(selecting at least 1 yellow marble) + P(selecting no yellow marbles) = 1

P(selecting at least 1 yellow marble) = 1 - P(selecting no yellow marbles)

Thus, if we can determine the probability that none of the 2 marbles selected are yellow, we’ll quickly be able to calculate the probability that at least one yellow marble is selected.

The bowl contains 8 marbles that are yellow, 6 that are blue, and 4 that are black, and we will select two of them. The probability that a non-yellow marble is selected first is 10/18 and the probability that a non-yellow marble is selected second is 9/17.

The probability that no yellow marbles are selected is: 10/18 x 9/17 = 5/1 x 1/17 = 5/17

Thus, the probability of selecting at least one yellow marble is: 1 - 5/17 = 12/17

Answer: B