Question

section 5.1 homework score: 3/17 answered: 3/17 question 4 a special deck of cards has 5 red cards, and 4 purple cards. the red cards are numbered 1, 2, 3, 4, and 5. the purple cards are numbered 1, 2, 3, and 4. 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(r) = round your answer to three decimal places. b. p(e) = round your answer to three decimal places. hint: sample space and probability video on probability + textbook

Explanation:

Step1: Calculate sample - space size

The total number of cards is the sum of red and purple cards. So, \(n = 5+4=9\).

Step2: Calculate \(P(R)\)

The probability of drawing a red card \(P(R)=\frac{\text{Number of red cards}}{\text{Total number of cards}}=\frac{5}{9}\approx0.556\).

Step3: Calculate \(P(E)\)

The even - numbered cards are red \(2,4\) and purple \(2,4\), so there are \(2 + 2=4\) even - numbered cards. Then \(P(E)=\frac{\text{Number of even - numbered cards}}{\text{Total number of cards}}=\frac{4}{9}\approx0.444\).

Answer:

a. 9
b. 0.556
c. 0.444