Question

a special deck of cards has 6 red cards, and 5 black cards. the red cards are numbered 1, 2, 3, 4, 5, and 6. the black cards are numbered 1, 2, 3, 4 and 5. the cards are well - shuffled and you randomly draw one card.
r = card drawn is red
e = card drawn is even - numbered
a. how many elements are there in the sample space?
b. p(e) = round your answer to two decimal places.
hint: sample space and probability
video on probability +
textbook

Explanation:

Step1: Calculate sample - space size

The sample space is the total number of cards. There are 6 red cards and 5 black cards. So the number of elements in the sample space is the sum of red and black cards.
$6 + 5=11$

Step2: Determine the number of even - numbered cards

The red cards are numbered 1, 2, 3, 4, 5, 6 and the black cards are numbered 1, 2, 3, 4, 5. The even - numbered cards are 2, 4, 6 from red cards and 2, 4 from black cards. So there are 3 + 2=5 even - numbered cards.

Step3: Calculate the probability of drawing an even - numbered card

The probability formula is $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the number of favorable outcomes (even - numbered cards) is 5 and the total number of outcomes (total cards) is 11. So $P(E)=\frac{5}{11}\approx0.45$

Answer:

a. 11
b. 0.45