Question

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?
enter an integer or decimal number more..
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. There are 5 red cards and 4 purple cards. So, the number of elements in the sample space $n(S)=5 + 4=9$.

Step2: Calculate $P(R)$

The probability of an event $P(A)=\frac{n(A)}{n(S)}$. For event $R$ (drawing a red card), $n(R) = 5$ and $n(S)=9$. So, $P(R)=\frac{5}{9}\approx0.556$.

Step3: Calculate $P(E)$

The even - numbered cards are red 2, 4 and purple 2, 4. So, $n(E)=4$. Then $P(E)=\frac{4}{9}\approx0.444$.

Answer:

a. 9
b. 0.556
c. 0.444