Question

Suppose that you have 11 cards. 6 are red and 5 are black. The 6 red cards are numbered 1,2,3,4,5 and 6. The 5 black cards are numbered 1, 2, 3,4, and 5. The cards are well-shuffled. You randomly draw one card.

• R = card drawn is red
• E = card drawn is even-numbered

Answer 1

To determine the probability of drawing a red card or an even-numbered card, we can use the formula:

P(R or E) = P(R) + P(E) - P(R and E)

We know that there are a total of 11 cards, so the probability of drawing any one card is 1/11.

The probability of drawing a red card is 6/11, since there are 6 red cards out of 11 total.

The probability of drawing an even-numbered card is 5/11, since there are 5 even-numbered cards out of 11 total.

To find the probability of drawing a red and even-numbered card, we need to consider that there are only three cards that satisfy this condition: the red cards numbered 2 and 4, and the black card numbered 2. Therefore, the probability of drawing a red and even-numbered card is 3/11.

Substituting these values into the formula, we get:

P(R or E) = 6/11 + 5/11 - 3/11

P(R or E) = 8/11

Therefore, the probability of drawing a red card or an even-numbered card is 8/11.