1. Section 5.3
Day 2

2. Page 311, E15
About 10% of high school girls report that they rarely or never wear a seat belt while riding in motor vehicles. Suppose you randomly sample four high school girls. Estimate the probability that no more than one of the girls says that she rarely or never wears a seat belt.
Assumptions?
Model?

3. Assumptions
probability of a randomly selected high school girl reporting that she rarely or never wears a seat belt is 10%

4. Assumptions
probability of a randomly selected high school girl reporting that she rarely or never wears a seat belt is 10%
the girls are selected independently of each other.

5. Simulation
About 10% of high school girls report that they rarely or never wear a seat belt while riding in motor vehicles. Suppose you randomly sample four high school girls. Estimate the probability that no more than one of the girls says that she rarely or never wears a seat belt.
(2) Model?

6. Model Outcomes: Reports she rarely or never wears a seat belt
Does not report she rarely or never wears a seat belt

7. Model Digits assigned to outcomes:
Reports she rarely or never wears a seat belt
Does not report she rarely or never wears a seat belt – 9
How many random digits constitute one run of the simulation?

8. Simulation
About 10% of high school girls report that they rarely or never wear a seat belt while riding in motor vehicles. Suppose you randomly sample four high school girls. Estimate the probability that no more than one of the girls says that she rarely or never wears a seat belt.
How many random digits constitute one run of the simulation?

9. Simulation
About 10% of high school girls report that they rarely or never wear a seat belt while riding in motor vehicles. Suppose you randomly sample four high school girls. Estimate the probability that no more than one of the girls says that she rarely or never wears a seat belt.
How many random digits constitute one run of the simulation?

10. Model Digits assigned to outcomes:
Reports she rarely or never wears a seat belt
Does not report she rarely or never wears a seat belt – 9
Select four digits, allowing repeats, and record the number of digits that are 0

11. A tetrahedral die has the numbers 1, 2, 3, and 4 on its faces
A tetrahedral die has the numbers 1, 2, 3, and 4 on its faces. Suppose you roll a pair of tetrahedral dice.
How many possible outcomes are there?

12. A tetrahedral die has the numbers 1, 2, 3, and 4 on its faces
A tetrahedral die has the numbers 1, 2, 3, and 4 on its faces. Suppose you roll a pair of tetrahedral dice.
How many possible outcomes are there?
4 ● 4 = 16

13. a. Make a two-way table of all 16 possible outcomes

15. b.Find P(sum of 6 or sum of 7) =

16. b. P(sum of 6 or sum of 7) = P(sum of 6) + P(sum of 7) =

17. c. Find P(doubles or sum of 7)

18. c. P(doubles or sum of 7) = P(doubles) + P(sum of 7) =

19. d. Can you use the Addition Rule of Disjoint Events to find P(doubles or a sum of 6)?

20. Can you use the Addition Rule of Disjoint Events to find P(doubles or a sum of 6)?
No, these events are not disjoint. The outcome (3, 3) is common to both.

21. The Addition Rule
How do you determine P(A or B) if A and B are not disjoint events?

22. The Addition Rule P(A or B) = P(A) + P(B) – P(A and B)
For any two events A and B,
P(A or B) = P(A) + P(B) – P(A and B)

23. P(doubles or a sum of 6)= P(doubles) + P(sum of 6) - P(doubles and a sum of 6) = ?

24. P(doubles or a sum of 6)= P(doubles) + P(sum of 6) - P(doubles and a sum of 6) = 4/16 + 3/16 – 1/16
= 6/16

25. Fill in the missing cells and marginal totals.
Owns a Laptop
Yes No
Total
Has a Dog 46 72
112
216

26. Fill in the missing cells and marginal totals.
Owns a Laptop
Yes No
Total
Has a Dog 26 46 72
112 32
144
138 78
216

27. Using the table, calculate the probability that a student randomly selected doesn’t have a dog or doesn’t own a laptop.
Owns a Laptop
Yes No
Total
Has a Dog 26 46 72
112 32
144
138 78
216

28. Using the table, calculate the probability that a student randomly selected doesn’t have a dog or doesn’t own a laptop. No double counting this way.
Owns a Laptop
Yes No
Total
Has a Dog 26 46 72
112 32
144
138 78
216

29. Use Addition Rule to calculate the probability that a student randomly selected doesn’t have a dog or doesn’t own a laptop.
Owns a Laptop
Yes No
Total
Has a Dog 26 46 72
112 32
144
138 78
216

30. Use Addition Rule to calculate the probability that a student randomly selected doesn’t have a dog or doesn’t own a laptop.
Owns a Laptop
Yes No
Total
Has a Dog 26 46 72
112 32
144
138 78
216

31. The Addition Rule
If you roll a pair of dice, find the probability you get doubles or a sum of 8.

32. The Addition Rule
If you roll a pair of dice, find the probability you get doubles or a sum of 8.
These are not disjoint as they have the common outcome (4, 4).

33. The Addition Rule
If you roll a pair of dice, find the probability you get doubles or a sum of 8.
P(doubles or sum of 8) = P(doubles) + P(sum of 8) – P(doubles and sum of 8)
= ?

34. The Addition Rule
If you roll a pair of dice, find the probability you get doubles or a sum of 8.
P(doubles or sum of 8) = P(doubles) + P(sum of 8) – P(doubles and sum of 8) =

35. The Addition Rule
If you roll a pair of dice, find the probability you get doubles or a sum of 8.
P(doubles or sum of 8) = P(doubles) + P(sum of 8) – P(doubles and sum of 8) =

36. Computing P(A and B)
In a local school, 80% of the students carry a backpack (B) or a wallet (W). Forty percent carry a backpack, and 50% carry a wallet. If a student is selected at random, find the probability that the student carries both a backpack and a wallet.

37. Computing P(A and B) Not disjoint, so
P(B or W) = P(B) + P(W) – P(B and W)
In a local school, 80% of the students carry a backpack (B) or a wallet (W). Forty percent carry a backpack, and 50% carry a wallet. If a student is selected at random, find the probability that the student carries both a backpack and a wallet.

38. Computing P(A and B) Not disjoint, so
P(B or W) = P(B) + P(W) – P(B and W)
Substitute known values:
0.80 = – P(B and W)
P(B and W) = ?

39. Computing P(A and B) Not disjoint, so
P(B or W) = P(B) + P(W) – P(B and W)
Substitute known values:
0.80 = – P(B and W)
P(B and W) = 0.10
Thus, the probability that a student carries both a backpack and a wallet is 10%.

40. Use the Addition Rule to compute the probability that if you flip two fair coins, you get heads on the first coin or you get heads on the second coin.

41. P(heads on first or heads on second ) =
P(heads on first) + P(heads on second ) – P(heads on both)
= ?

42. P(heads on first or heads on second ) =
P(heads on first) + P(heads on second ) – P(heads on both) =

43. Page 324, E33

44. Page 324, E33
Whistle?
Yes No Total
Yes
Swim? No
Total

45. Page 324, E33

46. Page 324, E33

47. Page 324, E33

48. Page 324, E33

49. Questions?
Quiz 5.1 – 5.3 Wednesday
One side of 4 x 6 note card