Question

A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Two marbles are drawn from the

bag.
Which expression represents the probability that one of the marbles is red and the other is blue?
O 30P2
O
50P2
0 3002
50C2
(10-1)(2001)
50C2
(1021)(20P1)
50P2

Answer 1

• (₁₀C₁) × (₂₀C₁)

₅₀C₂

Step-by-step explanation:

There are a total number of 10 + 15 + 5 + 20 = 50 marbles.

The number of ways in which any two marbles can be drawn is the combination of 50 marbles taken two at a time: ₅₀C₂, since the order does not matter.

There are 10 red marbles and 20 blue marbles.

Thus, the combinations with one red marble are: ₁₀C₁.

The combinations with one blue marble are: ₂₀C₁.

The combinations with one red and one blue marble is the product of the previous two:

• ₁₀C₁ × ₂₀C₁

Thus, the probability that one of the marbles is read and the other is blue is the quotient of the two sets:

• (₁₀C₁) × (₂₀C₁)

₅₀C₂