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A fair coin is tossed two ​times, and the events A and B are defined as...

A fair coin is tossed two ​times, and the events A and B are defined as shown below. Complete parts a through d.

A: {at most one tail​ is observed}

​B: {The number of tails observed is even​}

D. Find​ P(A), P(B), ​P(AU​B), P( Upper A Superscript c Baseline right parenthesis​, and ​P(An​B) by summing the probabilities of the appropriate sample points.

​P(A)= ? ​(Type an integer or simplified​ fraction.)

Find​ P(B). ​P(B)=? (Type an integer or simplified​ fraction.)

Find​P(Au​B). ​ P(Au​B)=? ​(Type an integer or simplified​ fraction.)

Find P(Ac) P(Ac)=? ​(Type an integer or simplified​ fraction.)

Find ​P(An​B). ​P(An​B)=? ​(Type an integer or simplified​fraction.) C.

Find ​P(AU​B) using the additive rule. Compare your answer to the one you obtained in part b.

​P(AU​B)=? (Type an integer or simplified​ fraction.)

Compare your answer to the one you obtained in part b. Choose the correct answer below.

A. The value of ​P(AU​B) calculated using the additive rule is less than ​P(AU​B) calculated by summing the probabilities of the sample points.

B. ​P(AU​B) calculated using the additive rule is greater than​P(AU​B) calculated by summing the probabilities of the sample points.

C. Both calculations of ​P(AU​B) produce the same result.

E. Are events A and B mutually​ exclusive? Why?

A. No​, events A and B are not mutually exclusive because​P(An​B)=0.

B. Yes​, events A and B are mutually exclusive because​P(AnB)=0.

C. No​, events A and B are not mutually exclusive because​P(An​B)not equal 0.

D. Yes​, events A and B are mutually exclusive because​P(An​B)not equals0.

Math   Statistics-And-Probability   
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According to the rules only first four subparts will be answered. Thankyou

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