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1 WORKSHEET 5: PROBABILITY Name: Section: Date: Answer the following problems and show computations on the blank spaces provided. 1. In a class there are 14 boys and 16 girls. What is the probability of selecting a girl in that class? 2. In rolling a pair of dice, what is the probability of getting A. a sum of 7? B. a sum of 5 or a sum of 9? C. a sum of 2 and a sum of 11? D. a sum of 1? 3. In selecting a card from a standard deck of 52 playing cards, what is the probability of getting a heart card and at the same time a face card? 4. In tossing three coins, what is the probability of getting A. exactly two heads? B. at least two heads? 5. A sample of 500 respondents was selected in a large city to determine information about consumer behavior. One of the questions asked was Do you enjoy shopping for clothing? Enjoys Shopping Male Female YES NO If an individual is chosen randomly from this group, find the probability that the person is A. a male and does not enjoy shopping B. a female or enjoys shopping C. does not enjoy shopping D. does not enjoy shopping given the consumer is a female
2 6. In a standard deck of 52 playing cards, 5 cards are to be selected. What is the probability that the cards selected contains A. two kings and three jacks? B. three heart cards? C. at least three queens? 7. In a standard deck of 52 playing cards, a card is to be selected. What is the probability that the card selected is a spade given that the card is a king, queen or jack? 8. Consider the word problem. What is the probability that a permutation of the word problem A. begins with a vowel? B. ends with a consonant? 9. In New York State, 48% of all teenagers own a skateboard and 39% of all teenagers own a skateboard and roller blades. What is the probability that a teenager owns roller blades given that the teenager owns a skateboard? 10. In a class of 30 students, there are 17 girls and 13 boys. Five are A students, and three of these students are girls. If a student is chosen at random, what is the probability of choosing a girl or an A student? 11. In the United States, 43% of people wear a seat belt while driving. If two people are chosen at random, what is the probability that both of them wearing a seat belt? 12. A jar contains 6 red balls, 3 green balls, 5 white balls and 7 yellow balls. Two balls are chosen from the jar, with replacement. What is the probability that both balls chosen are green? 13. Spin a spinner numbered 1 to 7, and toss a coin. What is the probability of getting an odd number on the spinner and a tail on the coin?
3 14. One bag contains 11 yellow balls and 7 blue balls and a second bag contains 8 yellow balls and 9 blue balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is blue? 15. In a 12item multiple choice examination (each with four choices of which only one is correct), what is the probability of getting only 4 mistakes assuming that no question is left unanswered? 16. If 6 balls are drawn without replacement from a bag that contains 7 black and 5 white balls, what is the probability that A. four will be black and 2 will be white? B. less than two white balls will be selected? C. There is at least one green black ball? 17. Four friends, Mark, Paolo, Kiko and JV decided to meet at Starbucks in Makati. Assuming that there are only four Starbucks outlets in the said city, what is the probability that A. all of them will meet in the same Starbucks outlet? B. three of the four will meet in the same Starbucks outlet and Mark is in another Starbucks outlet. 18. A committee of 5 members will be chosen from a group of 10 teachers and 5 students. What is the probability that the committee will have A. All teachers? B. 3 teachers and 2 students? C. 3 or 4 teachers? D. From 1 to 3 students?
4 19. In a university, 30% of the students major in Business Management, 25% major in Mathematics, and 10% major in both Business Management and Mathematics. A student from this university is selected at random. A. What is the probability that the student majors in Business Management or Mathematics? B. What is the probability that the student majors in neither of these two courses? C. If the student majors in Business Management, what is the probability that he/she also majors in Mathematics? 20. The probability that a man will live until 70 years is ¾ and the probability that his wife will live until 70 years is 4/5. What is the probability that A. Both will live until 70 years B. At least one will live until 70 years C. None will live until 70 years 21. A box contains 20 computer chips, 4 of which are defective. If 3 are selected at random, what is the probability that A. All are defective? B. At most one is defective? 22. Suppose that a company classifies 80% of its employees with good attendance and the rest with bad attendance. An employee is classified with good attendance if he/she is present and punctual 98% of the time. An employee is said to be with bad attendance if he/she is absent and late 30% of the time. What percentage of the total absences hold by employees classified as with bad attendance?
5 23. A box contains 4 black balls and 3 white balls, and another box contains 7 white balls and 3 black balls. If one ball is drawn from each box, what is the probability that the two balls are of different colors? 24. Suppose that in a certain town with a population of 5000 households, 3000 of the households have cell phone, 2000 have computers at home, and 1500 have both cell phones and computers. A household in the town is selected at random. A. What is the probability that the selected household owns a cell phone or a computer? B. What is the probability that the household does not own a cell phone or a computer? C. If the household owns a cell phone, what is the probability that it also owns a computer? D. If the household owns a cell phone, what is the probability that it does not own a computer? E. Is owning a cell phone independent of having a computer at home? Why? 25. Suppose that a bread manufacturing industry has three inspectors to stamp the expiration date on each package of bread. Ken, who stamps 20% of the packages, fails to stamp the expiration date once every 100 packages. Jen, who stamps 60% of the packages, fails to stamp once in every 200 packages. Kat, who stamps 20% of the packages, fails to stamp once in every 150 packages. A. What is the probability of getting a package with no expiration date? B. If a package has no expiration date, what is the probability that it was inspected by Jen? C. If a package has no expiration date, what is the probability that it was inspected by Ken or Kat?
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