5 If A and B are independent events with PA 005 and PB 065

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

5) since A and B are independent events then we have P(A/B) = P(A) i.e, 0.05

6) P(A) = 0.75   P(B) = 0.25 P(L/A) = 0.80 P(L/B) = 0.95

7) P(A/L) = P(A)*P(L/A)   divided by (sum of) P(A) P(L/A)+ P(B) *P(L/B)

                        (0.75)*(0.80)/ (0.75)(0.80)+(0.25)(0.95)

      answer is ( D)