A special deck of cards has 5 red cards, and 4 purple cards. The red cards...

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(E) = Round to 4 decimal places.

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Expert Solution

Given that a special deck of cards has 5 red cards and 4 purple cards. The red cards are numbered 1, 2, 3, 4, 5. The purple cards are numbered 1, 2, 3, 4. One card is randomly drawn. Given R = card drawn is red and E = card drawn is even numbered.

We know, Probability of any event = (Number of favorable outcomes)/(Total number of possible outcomes) ------(1)

a) Here, we have to find the number of elements in the sample space. We know, the total number of possible outcomes is the required number of elements in the sample space.

Here, total number of cards = 5 red + 4 purple = 5 +4 = 9. Thus, total number of possible outcomes = 9. --------(2)

Thus, the total number of elements in the sample space = 9.

Thus, there are 9 elements in the sample space.

b) Here, we have to find P(E). We know, E is the set of even numbered cards. We have to find the probability of getting an even numbered card.

Number of even numbered cards = 2 red[cards numbered 2,4] + 2 purple[cards numbered 2,4] = 2 + 2 = 4. Thus, number of favorable outcomes = 4. ---------(3)

Thus, from (1), (2) and (3), the required probability = 4/9 = 0.4444(rounded upto four decimal places).

Thus, the probability of getting an even numbered card = 0.4444 .

Thus, P(E) = 0.4444 .

orchestra answered 1 year ago

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