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.

Answer 1

Solution:

Given: 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.

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

Part a. How many elements are there in the sample space?

Sample Space is:

S = { R₁, R₂, R₃, R₄, R₅, R₆, B₁, B₂, B₃, B₄, B₅ }

Thus the number of elements in sample space are = N = 11

Part b) P(E) =..........?

P(E) =P( card drawn is even-numbered)

P(E) = Number of cards with even number / N

We have Even-numbered cards = {  R₂, R₄, R₆, B₂, B₄}

thus Even-numbered cards are 5.

Thus

P(E) = Number of cards with even number / N

P(E) = 5 / 11

P(E) = 0.4545

P(E) = 0.45