Question

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

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.

D. 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.

Answer 1

Solution :

1)

Probability of sample point = total sample point in event / Total sample space

· P(A) = ¾ =0.75

· P(B) = ¼ = 0.25

· P(AUB) = 4/4 =1

· P(Ac) = ¼ = 0.25

· P(A∩B) = 0/4 = 0

2)

find P(AUB) using additive rule

P(AUB) = P(A) + P(B) – P(A∩B)

=0.75 + 0.25 – 0
= 1

P(AUB) = 1

Option C is correct - Both calculations of P(AUB) produce the same results

3)

Are events A & B are mutually exclusive? Why?

Option B is correct - Yes. Events A & B are mutually exclusive because P(A∩B) = 0

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