Question

Consider a standard 52-card deck from which one card is randomly selected and not replaced. Then,...

  1. Consider a standard 52-card deck from which one card is randomly selected and not replaced. Then, a second card is randomly selected. Define the two events as given. Complete parts a) and b) below.

A = The first card is a club

B = The second card is a king

Are these two events mutually​ exclusive? Why or why​ not?

A.The events are not mutually exclusive. The event of selecting a club card as the first card cannot occur at the same time as selecting a king as the second card during the experiment.

B.The events are mutually exclusive. The event of selecting a club card as the first card can occur at the same time as selecting a king as the second card during the experiment.

C.The events not mutually exclusive. The event of selecting a club card as the first card cannot occur at the same time as selecting a king as the second card during the experiment.

D.The events are not mutually exclusive. The event of selecting a club card as the first card can occur at the same time as selecting a king as the second card during the experiment.

Are these two events​ independent? Why or why​ not?

A.The events are not independent. Selecting a club the first time does not influence the probability of selecting a king the second time.

B.The events are not independent. Selecting a club the first time influences the probability of selecting a king the second time.

C.The events are independent. Selecting a club the first time influences the probability of selecting a king the second time.

D.The events are independent. Selecting a club the first time does not influence the probability of selecting a king the second time.

Math   Statistics-And-Probability   
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Answer #1

The given events are

The probabilities for (selection without replacement) are

These two events mutually​ exclusive since . Or the explanation is

D).The events are not mutually exclusive. The event of selecting a club card as the first card can occur at the same time as selecting a king as the second card during the experiment.

The events are independent since . Or the explanation is

D).The events are independent. Selecting a club the first time does not influence the probability of selecting a king the second time.

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