Probability Chapter 11 1

Conditional Probability Section

Conditional Probability  If A and B are events in a sample space U and P(B) ≠ 0, the conditional probability of A, given B, is denoted by P(A|B) and is defined by 3

Examples A family has 3 children. If each of the outcomes is equally likely, find the probability that the family has 3 girls given that a. the first child is a girl. b. the first child is a boy. c. the first and second child are girls. 4

Examples A recent survey of 400 instructors at a major university revealed the data shown in the following table. Based on the data, what are the probabilities of the following? a. An instructor received a good evaluation, given the instructor was tenured. b. An instructor received a poor evaluation, given the instructor was tenured. 5

Solutions Status Good Evaluations Poor Evaluations Tenured72168 Nontenured8476 6

Example:  Companies A, B, and C produce 29%, 24%, and 47% respectively of the major appliances sold in a certain area. In that area, 1.90% of the Company A appliances, 2.30% of the Company B appliances, and 1.20% of the Company C need service within the first year. Suppose an appliance that needs service within the first year is chosen at random, find the probability it was manufactured by Company A. 7

Solution: Co. A service Co. B service Co. C service

Example:  The student body at Overpower Tech is 46% male. Although 37% of the men major in business, only 21% of the women select that major. Find the probability that a non business major is a man. 9

Solution: men businessnot business women businessnot business Notice that the branches always add to give a sum of one.

Examples  Two dice were thrown, and a friend tells us that the numbers that came up were different. Find the probability that the sum of the numbers was a. 4.b. 7. c. an even number. d. an odd number. 11

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Solutions 13 END