From a jar containing 4 red and 2 white marbles, Lionel draws two marbles simultaneously and at random. What is the prob

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:21 am

From a jar containing 4 red and 2 white marbles, Lionel draws two marbles simultaneously and at random. What is the probability that he picks one marble of each color?

A. 3/5
B. 8/15
C. 7/15
D. 2/5
E. 7/30

Answer: B
Source cold and Veritas Prep

P(one of each color) = P(1st is red AND 2nd is white OR 1st is white AND 2nd is red)
= P(1st is red AND 2nd is white) + P(1st is white AND 2nd is red)
= [P(1st is red) x P(2nd is white)] + [P(1st is white) x P(2nd is red)]
= [4/6 x 2/5]+ [2/6 x 4/5]
= 8/30+ 8/30
= 16/30
= 8/15

Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:21 am

From a jar containing 4 red and 2 white marbles, Lionel draws two marbles simultaneously and at random. What is the probability that he picks one marble of each color?

A. 3/5
B. 8/15
C. 7/15
D. 2/5
E. 7/30

Answer: B

Solution:

The number of ways he can choose 2 marbles is 6C2 = (6 x 5)/2 = 15. The number of ways he can choose 1 marble of each color is 4C1 x 2C1 = 4 x 2 = 8. Therefore, the probability of picking one marble of each color is 8/15.

Alternate Solution:

Lionel can choose either R-W or W-R. The probability of R-W is 4/6 x 2/5 = 8/30 = 4/15, and the probability of W-R is 2/6 x 4/5 = 8/30 = 4/15. Thus, the probability of picking one marble of each color is 4/15 + 4/15 = 8/15.

Answer: B