1 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt Probably So And Or Not You Can Count On It A Roll of the Dice Probability Potpourri

2 You roll a die. What is the probability that you get a 5?

3 1/6

4 You flip two coins. What is the probability that you get two tails?

5 P(T,T) P(T)P(T) ½ * ½ =1/4

6 You flip two coins. What is the probability that you get at least one Tails ?

7 1 – P(H,H) 1 – P(H)P(H) 1 – ½ * ½ 1 – ¼ =3/4

8 You draw one card from a deck. What is the probability that it is a red face card? (consider aces as face cards)

9 8/52 = 2/13

10 You run a poll to see where people buy groceries. Here are your results: Store# of Shoppers Wal-Mart10 Kroger8 Target3 Meijer1 Based on your data. If you ask a person at random, what is the probability that they buy groceries at somewhere besides Wal-Mart?

11 (8+3+1)/22 = 12/22 = 6/11 or 1 – (10/22) = 12/22 = 6/11

12 Which pair of events is NOT mutually exclusive? A) being male, being female B) drawing a king, drawing a queen C) being male, being a sophomore D) picking a red M&M, picking a green M&M

13 C) Being a male, being a sophomore

14 You draw one card, look at it, and replace it. Then you draw a second card. What is the probability that: you draw a king followed by a queen

15 INDEPENDENT “AND” EVENTS P(K, Q) P(K)*P(Q) (4/52)*(4/52) = 1/169 =.0059

16 If you choose a person in class at random, the probability that they are a senior is 52%. The probability that the person is a freshman is 21%. What is the probability that the person you select is a freshman OR a senior?

17 Mutually Exclusive Events P(F OR Sr) P(F) + P(Sr) 52% +21% =73%

18 You draw a single card from a deck of 52. What is the probability that you get a face card or a diamond?

19 NOT Mutually Exclusive! P(Face OR Diamond) P(Face) + P(Diamond) – P(Face & Diamond) (16/52) + (13/52) – (4/52) = 25/52 =0.481

20 You draw two cards without replacement. What is the probability that they are not both face cards?

21 1 – P(Face, Face) 1 – (16/52)(15/51)= 1 – (240/2652) 1 –

22 Compute this:

23

24 You are taking a 10 problem multiple choice test. There are 4 choices for each question. How many different ways could you complete the test?

= 1,048,576

26 Dunbar is hiring 4 new janitors, but 10 people have applied for the jobs. How many different ways could the school fill the 4 positions?

27

28 There are 10 math teachers at Dunbar, and only 7 classrooms. How many ways could classrooms be assigned to teachers?

29

30 You are going on a trip and can only take 4 friends. There are 7 guys and 5 girls in consideration for the trip. If you select the group completely at random, what is the probability that you select all girls?

31

32 You roll two dice. What is the probability that you get two sixes?

33 P(6,6) P(6)*P(6) (1/6)(1/6) = 1/36

34 You are playing Yahtzee. (Each turn you roll 6 dice.) On any given turn, what is the probability that you will get all 1’s?

35 (1/6) 6 = 1/46656

36 You roll two dice. What is the probability that you will get a sum of 6?

37 Die 1Die P(sum of 6) = 5/36

38 You roll a single die. What is the probability of that you get an even number or a multiple of 3?

39 P(even OR mult of 3) P(even) + P(mult of 3) – P(even)*P(mult of 3) 3/6 + 2/6 – (3/6)(2/6) 3/6 + 2/6 – 1/6 4/6 = 2/3

40 You roll two dice. What is the probability that you do not get two even numbers?

41 1 – P(even)*P(even) 1 – (1/2)(1/2) 1 – 1/4 = 3/4 or P(odd,even OR even,odd OR odd, odd) P(odd,even) + P(even, odd) + P(odd, odd) (1/2)(1/2) + (1/2)(1/2) + (1/2)(1/2) ¼ + ¼ + ¼ = 3/4

42 You flip a coin 4 times. What is the probability that you get 4 Heads?

43 P(H,H,H,H) P(H)*P(H)*P(H)*P(H) (1/2)(1/2)(1/2)(1/2) (1/2) 4 = 1/16

44 Which of the following are NOT independent events? a) Flipping two coins b) Drawing two cards without replacement c) Rolling two dice d) Choosing two random numbers

45 b) Drawing two cards without replacement

46 You are rolling two dice. What is the probability that you get a sum of 3?

47 P(1,2 OR 2,1) P(1,2) + P(2,1) (1/6)(1/6) + (1/6)(1/6) (2/36) = 1/18

48 There are 23 people in class. A class poll gave the following results: 10 students are taking Geometry 6 students are taking Band 3 of these students are enrolled in both. If you choose a student at random, what is the probability that are a Band student OR a Geometry student?

49 (10/23) + (6/23) – (3/23) = 13/23

50 You draw two cards at random. What is the probability that you get 21? (one of the two cards is an ace & the other is a 10, jack, queen, or king) Hint: you could get the Ace first OR the face card first.

51 P(ace, 10 value) OR P(10 value, ace) P(ace)P(10 value) + P(10 value)P(ace) (4/52)(16/51) + (16/52)(4/51) = (64/2652) + (64/2652) = = 0.048

52 FINAL JEOPARDY!! You are playing BlackJack (just you vs. the dealer). You have an Ace and a 5. You notice that he is “showing” an Ace. If neither of you take another card, what is the probability that you beat the dealer? Hint: You’re looking for the probability that the hidden card is a… Hint 2: How many cards are unaccounted for?

53 Probability that the hidden card is a: Ace OR 2 OR 3 OR 4 2/49 + 4/49 + 4/49 + 4/49 14/49 = 2/7