5-If A A and B B are two mutually exclusive events with P(A)=0.5 P ( A ) = 0.5 a

Question

5-If A A and B B are two mutually exclusive events with P(A)=0.5 P ( A ) = 0.5 and P(B)=0.4 P ( B ) = 0.4 , find the following probabilities:

a)P(AB)=P(AB)=

b)    P(AB)=P(AB)=

c)   P(Ac)=P(Ac)=

d)   P(Bc)=P(Bc)=

e)   P(AB)c=P(AB)c=

f)   P(ABc)=

3)Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing each of the following events:

A:{A:{ A 3 does not appear on either die }}
B:{B:{ The sum of the numbers is even }}
C:{C:{ The sum of the numbers is equal to 7 }

P(A)=

P(B)=

P(C)=

2) A triangular die is a four-sided die, each side possessing either a number 1, 2, 3, or 4. Two such die are tossed simultaneously and the bottom faces - the face that each die lands on - is observed. Consider the following events:

AA the bottom-most faces sum to six
BB each bottom-most face shows an even number
CC both bottom-most faces show the same number, referred to as doublesdoubles

Part (a) What is the probability that the bottom-most faces do not sum to six? (Use four decimals in your answer)

Part (b) Find P(AB)P(AB) (Use four decimals)

Part (c) Find P(ACCc)P(ACCc) (use four decimals)

Part (d) Find P(ABC)P(ABC) (use four decimals)

Part (e) Are the events AA and CC mutually exclusive events? Select the most appropriate reason below.
A. AA and CC are mutually exclusive events because they are not independent events.  
B. AA and CC are mutually exclusive events because P(AC)=0P(AC)=0.  
C. AA and CC are not mutually exclusive events because P(AC)=P(A)P(C)P(AC)=P(A)P(C).  
D. AA and CC are not mutually exclusive events because P(AC)P(A)P(C)P(AC)P(A)P(C).  
E. AA and CC are not mutually exclusive events because P(AC)0P(AC)0

6)If P(A)=0.7,P(A)=0.7, P(B)=0.45P(B)=0.45 and P(AB)=0.2,P(AB)=0.2, find the following probabilities:
a)   P(AB)=P(AB)=

b)   P(Ac)=P(Ac)=

c)   P(Bc)=P(Bc)=

d)   P(ABc)=P(ABc)=

e)   P(AB)c=

12) A pool of potential jurors consists of 16 men and 15 women. 10 jurors are to be chosen at random from the pool of 31.

What is the probability that this jury is made up
Part (a) 2 men? (use four decimals)

Part (b) half of the jury are men and half are women? (use four decimals)

Part (c) at least two women are amongst the 10 jurors? (use four decimals)

Part (d) The jury has been selected and there are 10 men on the jury. Assuming the jury was chosen randomly, what is the chance of this occurring?

P(10men)=P(10men)= use four decimals)

Part (e) Consider the jury selection that occurred in part (d) and the probability this happening. Would you this particular jury cause you to question the randomness of the jury selection? That is, can the 10 men on the jury lead you to be suspicious about the randomness of the jury selection?
A. Yes, because the chance of 10 men being chosen on the jury is not likely if the jury selection were random.
B. No, because the chance of 10 men being chosen on the jury is likely if the jury selection were random.
C. Yes, because the chance of 10 men being chosen on the jury is likely if the jury selection were random.
D. No, because the chance of 10 men being chosen on the jury is not likely if the jury selection were random.

Explanation / Answer

(According to Chegg policy, only one questions with four subquestions will be answered. Please post the remaining in another question)

5 P(A) = 0.5 and P(B) = 0.4

a) P(A B) = 0, since the events are mutually exclusive.

b) P(A B) = P(A) + P(B) = 0.5 + 0.4 = 0.9

c) P(Ac) = 1 - P(A) = 1 - 0.5 = 0.5

d) P(Bc) = 1 - P(B) = 1 - 0.4 = 0.6

e) P(A B)c = 1 - P(A U B) = 1 - 0.9 = 0.1

f)   P(A Bc) = P(A) - P(A B) = 0.5 - 0 = 0.5

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