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Find the probability of disjoint and overlapping events., Summaries of Statistics

University of California - Los Angeles (UCLA)Statistics

What is the probability that a randomly selected senior is both a varsity and on the honor roll? Page 3. 3. Exercise 1: Find each of the probabilities a) ...

Typology: Summaries

2022/2023

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Lesson 51 Trigonometry Name:_______________________
Mr. Jones Date:___________________
S.W. B. A. T: Find the probability of disjoint and overlapping events.
DO NOW: The numbers 2, 4, 5, 6, 9, 10, 11, 14 are in a hat. You will reach in the hat to
pick a number once. What is the probability of each?
a) An odd number or a number greater than 6
b) A multiple of 2 or a multiple of 3
Definitions
Disjoint or mutually exclusive are two events that have no outcomes in common.
P(A or B) = P(A) + P(B)
Overlapping events are two events that have one or more outcomes in common.
P(A or B) = P(A) + P(B) – P(A and B)
Example 1: Find each of the probabilities.
a) Events A and B are disjoint. P(A) = 2
3 and P(B) = 1
6. Find the P (A or B).
pf3
pf4
pf5

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Lesson 51 Trigonometry Name:_______________________ Mr. Jones Date:___________________

S.W. B. A. T: Find the probability of disjoint and overlapping events.

DO NOW: The numbers 2, 4, 5, 6, 9, 10, 11, 14 are in a hat. You will reach in the hat to pick a number once. What is the probability of each? a) An odd number or a number greater than 6 b) A multiple of 2 or a multiple of 3 Definitions Disjoint or mutually exclusive are two events that have no outcomes in common. P(A or B) = P(A) + P(B) Overlapping events are two events that have one or more outcomes in common. P(A or B) = P(A) + P(B) – P(A and B) Example 1 : Find each of the probabilities. a) Events A and B are disjoint. P(A) = 2 3 and P(B) = 1 6

. Find the P (A or B).

b) Events are overlapping. Find P(A or B). P(A) = 7 20 P(B) = 9 20 P(A and B) = 3 20 c) Events are overlapping. Find P(A and B). P(A) = 12 52 P(B) = 13 52 P(A or B) = 22 52 d) Out of 200 students in a senior class, 113 students are either varsity athletes or on the honor roll. There are 74 seniors who are varsity athletes and 51 seniors who are on the honor roll. What is the probability that a randomly selected senior is both a varsity and on the honor roll?

d) Out of 45 customers at a breakfast café, 42 customers bought coffee or orange juice. There were 30 customers who bought orange juice and 40 customers who brought coffee. What is the probability that a randomly selected customer brought both coffee and orange juice?

EXIT

  1. A bag contains cards numbered 1 through 20. One card is randomly selected. a) What is the probability that the number on the card is a multiple of 3 or a multiple of 4? b) A second card is selected after the first card is replaced. What is the probability that the number on the card is a multiple of 3 and a multiple of 4?
  2. Given the trigonometry function y = 3 sin x – 3, find the amplitude, period, quarter cycle, and the five key x-values.

c) P(B) = 1 9 , P(A and B) = 3 36 , P(A or B) = 7 36

4. Form 3C is looking for a new monitor. The probability of either John or Jenny

being the monitor is 0.6. The probability of John becoming the monitor is 0.2.

What is the probability of Jenny becoming the monitor?

5. A group of 40 trees in a forest are not growing properly. A botanist

determines that 34 of the trees have a disease or are being damaged by insects.

With 18 trees having a disease and 20 being damaged by insects. What is the

probability that a randomly selected tree has both a disease and is being damaged

by insects?