3 If A and B are mutually exclusive events with PA 03 and P

3.  If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A U B) =

A) 0.30

B) 0.15

C) 0.00

D) 0.8

E) None of the above

4. A six-sided die is tossed three times.  The probability of observing three ones in a row is

A) 1/3

B) 1/6

C) 1/27

D) 1/216

E) None of the above

5. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then  P(A l B) =

A) 0.05

B) 0.0325

C) 0.65

D) 0.8

E) None of the above

6. Two methods, A and B, are available for teaching a certain industrial skill. There is an 80% chance of successfully learning the skill if method A is used, and a 95% chance of success if method B is used. However, method B is substantially more expensive and is therefore used only 25% of the time (method A is used the other 75% of the time). The following notations are suggested:

A—method A is used

B—method B is used

L—the skill was Learned successfully

Which of the following is the correct representation of the information that is provided to us?

A) P(A) = 0.75, P(B) = 0.25, P(L | A) = 0.80, P(L | B) = 0.95

B) P(A) = 0.75, P(B) = 0.25, P(A | L) = 0.80, P(B | L) = 0.95

C) P(A) = 0.75, P(B) = 0.25, P(A and L) = 0.80, P(B and L) = 0.95

D) P(A | L) = 0.75, P(B | L) = 0.25, P(L | A) = 0.80, P(L | B) = 0.95

E) P(A and L) = 0.75, P(B and L) = 0.25, P(L | A) = 0.80, P(L | B) = 0.95

7. Two methods, A and B, are available for teaching a certain industrial skill. There is an 80% chance of successfully learning the skill if method A is used, and a 95% chance of success if method B is used. However, method B is substantially more expensive and is therefore used only 25% of the time (method A is used the other 75% of the time). The following notations are suggested:

A—method A is used

B—method B is used

L—the skill was Learned successfully

A worker learned the skill successfully. What is the probability that he was taught by method A?

A) 0.75 * 0.80 = 0.60

B) 0.80

Solution

3.

As they are mutually exclusive,

P(A and B) = 0

Thus,

P(A U B) = P(A) + P(B) - P(A and B)

= 0.3 + 0.5 - 0

= 0.8 [ANSWER, D]

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4.

The probability of observing a 1 is 1/6.

Thus, the probability of three ones in a row is (1/6)(1/6)(1/6) = 1/216. [ANSWER, D]

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