Download presentation
Presentation is loading. Please wait.
Published byRudolf Hancock Modified over 9 years ago
1
Bell Work: Factor x – 6x – 16 2
2
Answer: (x – 8)(x + 2)
3
Lesson 70: Probability and Designated Order
4
The study of probability began when people began studying games of chance such as flipping coins, rolling dice, drawing cards from a deck, or drawing marbles from an urn. Problems from games of chance still provide the best models on which to base a study of elementary probability, and we will concentrate on these problems.
5
The study of probability is based on the study of outcomes that have an equal chance of occurring.
6
It is customary to call activities such as flipping coins, rolling dice, blindly selecting cards from a deck, and drawing marbles from an urn experiments and to call the individual results outcomes.
7
We call the set of equally probable outcomes the sample space for the experiment. A toss of a fair coin has two equally probable outcomes. Thus, the sample space for a coin toss is heads or tails, as shown below. HT
8
The roll of a single die has six equally probable outcomes. Thus, the figure below shows the sample space for the roll of a single die. 123456
9
We define the probability of a particular even as the number of outcomes that satisfy the requirement divided by the total number of outcomes in the sample space. particular event=number outcomes that satisfy requirement total number of outcomes in sample space
10
The probability of any event is a number between 0 and 1 inclusive. If no outcomes satisfy the requirement, the probability is 0, and if every outcome satisfies the requirement, the probability is 1.
11
Thus we see that a probability of - 2 of 7 ½ is not possible because the probability of any event must be a number between 0 and 1.
12
Example: A fair coin is tossed three times and comes up heads every time. What is the probability that on the next toss it will come up heads?
13
Answer: P = number of outcomes outcomes in sample space P = ½
14
Example: Six green marbles and eight red marbles are placed in an urn. One marble is drawn and then dropped back in the urn. Then a second marble is drawn and dropped back into the urn. Both marbles were red. If another marble is drawn, what is the probability that it will be red?
15
Answer: P = 8/14 = 4/7
16
Practice: A single die is rolled three times. The results are 1, 4, and 3, in that order. What is the probability that the next roll will produce a number greater than 2?
17
Answer: 4/6 = 2/3
18
Practice: Two dice are rolled. What is the probability that the sum of the numbers rolled is 7 A number greater than 8
19
Answer: 6/36 = 1/6 10/36 = 5/18
20
Designated Order: The probability of future outcomes of independent events happening in a designated order is the product of the probability of the individual outcomes.
21
For example, if we toss a coin twice, the probability of getting a heads on the first toss and a tails on the second toss is one fourth. P(H, T) = P(H) x P(T) = ½ x ½ = ¼
22
Example: A fair coin is tossed four times. What is the probability that the first two times it comes up heads and the last two times it comes up tails?
23
Answer: ½ x ½ x ½ x ½ = 1/16
24
Practice: The spinner show is spun twice. What is the probability that the spinner stops on 4 and then on 3?
25
Answer: ¼ x ¼ = 1/16
26
HW: Lesson 70 #1-30
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.