Question

19-28: Theoretical Probabilities. Use the theoretical method to determine the probability of the following outcomes and events. State any assumptions that you make.

19. Tossing two coins and getting either no tails or one tail

20. Rolling a single die and getting an even number (2, 4, or 6)

21. Drawing a king from a standard deck of cards

22. Drawing a red card (heart or diamond) from a standard deck of cards

23. Randomly selecting a two-child family with two boys

24. Randomly selecting a three-child family with exactly two boys

25. A randomly selected person has a birthday in April.

26. A randomly selected person has a birthday in a month beginning with J.

27. Sharing a birthday with another person when you both have birthdays in December

Answer 1

Theoretical probability is a method to express the likelihood that something will occur. It is calculated by dividing the number of favorable outcomes by the total possible outcomes.

19. The number of total possible outcomes when tossing two coins is 4. While the number of favorable outcomes of getting either no tails or one tail is 3{HT, TH, HH}. Thus the theoretical probability is 3/4 = 0.75

20. The number of total possible outcomes while rolling dice is 6. The number of favorable outcomes for getting an even number is 3. thus the theoretical probability is 3/6 = 0.5

21. The number of total possible outcomes in a standard deck of card= 52. The number of favorable outcomes for getting a king is 4. Thus the theoretical probability of the event is 4/52 = 1/13.

22. The number of total possible outcomes in a standard deck of card = 52. The number of favorable outcomes for getting a red card is 26. Thus the theoretical probability of the event is 26/52 = 0.5.

23. Here we can assume that girls and boys have the same occurrence probability. The number of total possible outcomes for a two-child family= 4. The number of favorable outcomes for the two boys is 1. Thus the theoretical probability of the event is 1/4 = 0.25

24. Here we can assume that girls and boys have the same occurrence probability. The number of total possible outcomes for a three-child family= 4. The number of favorable outcomes for the two boys is 3. Thus the theoretical probability of the event is 3/8 = 0.375

25. Here we can assume that occurrence of birthdays for a person is uniformly distributed. Then the number of possible outcomes for a birthday is 365. The number of favorable outcomes for a birthday in April is 30. Thus the theoretical probability of the even is 30/365.

26. Here we can assume that occurrence of birthdays for a person is uniformly distributed. Then the number of possible outcomes for a birthday is 365. The number of favorable outcomes for a birthday in a month beginning with J(January, June, and July) is 31+30+31 = 92. Thus the theoretical probability of the even is 92/65.

27. Here we can assume that occurrence of birthdays for a person is uniformly distributed. Then the number of possible outcomes for a birthday is 365. The number of favorable outcomes for sharing a birthday in December is 31. Thus the theoretical probability of the even is 31/365.