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MA 321 Probability&Statistics Basic Probability Worksheet 1 Dr. Lisa M.James Spring 2019 Instructions: On a separate sheet of paper, respond to the following problems. Only neat work will be accepted. All pages submitted should have straight edges 1. A couple is planning to have 3 children and are concerned with what the gender of their children will be. a. What is the sample space S of the above experiment? Use B for boy and G for girl. b. What is the event A that a boy is the first child to be born? 2. A pair of fair dice is rolled. a. What is the sample space S? b. What is the probability of each of the outcomes? c. Find the probability that the sum of the dice is 8. d. In how many ways can doubles (both dié having the same number) be rolled? 3. The table below represents the sample space S for selecting one card from a deck of 52 cards. A 2 3 4 5 6 7 89 10JQ K a. What is the probability that a card selected from the deck is a heart? b. What is the probability that a card selected from the deck is a Jack or an 8? c. What is the probability that a card selected from the deck is a diamond and a club? 4. Oakwood University Dining Hall offers the following breakfast menu options 2
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1. A couple is planning to have 3 children (can be either one of 2), so number of possible combinations of 3 children would be 2 2*2 a. The sample space would be 8 S (BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG) b. The event A that a boy is the first child would be A (BBB, BBG, BGB, BGG 2. If a pair of fair dice rolled (which has 6 sides); number of possible outcomes would be 6*6 - 36 a. The sample space would be b. Each of these 36 would have equal chance of occurrence (since dice are fair), so probability of each of these outcomes would be 1/36 In a sample space of 36 elements; (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) these 5 elements has the sum 8, so the probability that the sum of dice is 8 would be 5/36 C. d. From the sample space we can see (1,1) (2,2) (3, 3) (4, 4) (5, 5) (6, 6) in 6 ways doubles can be rolled 3. a. In a deck of 52 cards there are 13 heart cards, so probability that a selected card from the deck is heart would be 13/52 1/4 b. in a deck of 52 cards there are 4 Jacks and 4 8s, i.e. 8 cards which are Jack or an 8, so the probability that a selected card from the deck is a Jack or an 8 would be 8/52 - 2/13 c. In a deck of 52 cards, we dont have any card that is diamond as well as club (intersection of diamond and club is O), so probability that a selected card from the deck is diamond and a club would be 0

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