Conditional Probability Worksheet #3 𝑃(𝐴|𝐵) = P( A  B) or P( B) 𝑃(𝐴 𝑎𝑛𝑑 𝐵) 𝑃(𝐵) or Name _______________________ 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝐴 𝑎𝑛𝑑 𝐵 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝐵 Exercises 7-10, use the data in the table below, which shows the employment status of individuals in a particular town by age group. Age Group 0-17 18-25 26-34 35-49 50+ Totals: Full-time 24 185 348 581 443 Part-time 164 203 67 179 162 Unemployed 371 148 27 104 173 Totals: 7. If a person in this town is selected at random, find the probability that the individual is employed parttime, given that he or she is between the ages of 35 and 49. 8. If a person in the town is randomly selected, what is the probability that the individual is unemployed, given that he or she is over 50 years old? 9. A person from the town is randomly selected; what is the probability that the individual is employed fulltime, given that he or she is between 18 and 49 years of age? 10. A person from the town is randomly selected; what is the probability that the individual is employed part-time, given that he or she is at least 35 years old? Exercises 11-14, use the data in the following table, which shows the results of a survey of 2000 gamers about their favorite home video game systems, organized by age group. If a survey participant is selected at random, determine the probability of each of the following. 0-12 13-18 19-24 25+ Totals Sony PlayStation 2 63 105 248 191 607 Microsoft Xbox 84 139 217 166 606 Nintendo GameCube 55 92 83 88 318 Sega Dreamcast Totals 51 253 113 449 169 717 136 571 469 2000 11. The participant prefers the Sony PlayStation 2 system. 12. The participant prefers the Microsoft Xbox, given that the person is between the age of 13 and 18. 13. The participant prefers Nintendo GameCube, given that the person is between the ages of 13 and 24. 14. The participant is between 0 and 12 years of age, given that the person prefers the Sega Dreamcast machine. 15. A pair of dice are tossed. Find the probability that the sum on the two dice is 8, given that the sum is even. 16. A pair of dice are tossed. Find the probability that the sum on the two dice is 12, given that doubles are rolled. 17. A pair of dice are tossed. What is the probability that doubles are rolled, given that the sum on the two dice is less than 7? 18. A pair of dice are tossed. What is the probability that the sum on the two dice is 8, given that the sum is more than 6? Remember: 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵) 19. What is the probability of drawing two cards in succession (without replacement) from a standard deck and having them both be face cards? 20. Two cards are drawn from a standard deck without re- placement. Find the probability that both cards are hearts. 21. Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a spade and the second card is red? 22. Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a king and the second card is not? In Exercises 23-26, a snack-size bag of M&Ms candies is opened. Inside, there are 12 red candies, 12 blue, 7 green, 13 brown, 3 orange, and 10 yellow. Three candies are pulled from the bag in succession, without replacement. 23. Determine the probability that the first candy drawn is blue, the second is red, and the third is green. 24. Determine the probability that the first candy drawn is brown, the second is orange, and the third is yellow. 25. What is the probability that the first two candies drawn are green and the third is red? 26. What is the probability that the first candy drawn is orange, the second is blue, and the third is orange? In Exercises 27-30, three cards are dealt from a shuffled standard deck of playing cards. 27. Find the probability that the first card dealt is red, the second is black, and the third is red. 28. Find the probability that the first two cards dealt are clubs and the third is a spade. 29. What is the probability that the three cards dealt are, in order, an ace, a face card, and an 8? (A face card is a jack, queen, or king.) 30. What is the probability that the three cards dealt are, in order, a red card, a club, and another red card?