Question

In a box there are 3 red cards and 5 blue cards. The red cards are marked with the

numbers 1, 2, and 3, and the blue cards are marked with the numbers 1, 2, 3, 4, and
5. The cards are well-shuffled. You reach into the box (you cannot see into it) and
draw one card.
Here is the sample space: S = { R1, R2, R2, B1, B2, B3, B4, B5)
Let, A = blue card is drawn and E = even-numbered card is drawn.
Find P(EA).
[In words, If you draw a blue card, what is the probability that it shows an even
number?]
a. 2/3
b. 3/8
c. 0
d. 2/5

Answer 1

To find the probability of drawing an even-numbered card given that a blue card is drawn, P(E|A), we count the even-numbered blue cards (B2, B4) and divide by the total number of blue cards, resulting in P(E|A) = 2/5. The correct multiple-choice option is (d).

Step-by-step explanation:

The given problem is a question of conditional probability in which we are interested in finding P(E|A), the probability of drawing an even-numbered card given that a blue card is drawn. Since we have three red cards marked 1, 2, and 3, and five blue cards marked 1, 2, 3, 4, 5, the relevant events here are A (blue card is drawn) and E (even-numbered card is drawn).

To find P(E|A), we first determine the number of blue cards which are also even-numbered. From the blue cards, B2 and B4 are even-numbered. There are a total of 5 blue cards, which means there are 2 favorable outcomes of drawing an even-numbered blue card out of the 5 blue cards.

Therefore, the probability P(E|A) is 2 (favorable outcomes: B2, B4) divided by 5 (total blue cards): P(E|A) = 2/5. The correct multiple-choice option is (d).