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Lesson 3 Unit 2 Probability Couplements, Disjoint Events and the addition Rule
1.M&M candies are great for probability. The following tables are the color distributions for the candies. Fill in each table with the missing probability and answer the questions that follow.
Plain Brown Blue Green Orange Red Yellow
Probability 0.3 0.1 0.1 0.1 0.02 ???
Peanut Brown Blue Green Orange Red Yellow
Probability 0.2 0.3 0.1 0.1 0.01 ???
a) What is the probability that a plain M&M is red or blue? = 0.02+0.1=0.12
b) b) What is the probability that a peanut M&M is not brown? = 0.01+0.3=0.31
2. In order to ensure the safety of school classrooms the local Fire Marshall does an inspection at Thomas Jefferson High School every month, looking for faulty wiring, overloaded circuits, etc. At TJHS the new Academic Wing has 5 math rooms, 10 science rooms, and 10 English rooms. The science rooms are divided into 8 biology and 2 chemistry rooms. Each month, the Fire Marshall randomly picks one of the rooms in the new wing to inspect each month. Define the following events:
S = the event the selected room is a science room
B = the event the selected room is a biology room
M = the event the selected room is a math room
E = the event the selected room is an English room
C = the event the selected room is a chemistry room
Calculate the probabilities of the events described below:
a) P(S) - 10/25
b) P(M or E) - 15/25
c) P(E or B -18/25
) d) P(S and not C) -8/25
3. Research shows that the probability of dying from heart disease is o.45 and the probability of dying from cancer is 0.22.
a. What is the probability that a death was due to either heart disease or cancer 0.45+.22= 67 or 67%
b. What is the probability that a death was due to some other cause? 100-67=33 or 33%
For question 1:
To fill in the missing probabilities in each table, you can calculate them by subtracting the sum of the given probabilities in each table from 1. For example, in the Plain M&M table, the sum of the given probabilities is 0.8 (0.3 + 0.1 + 0.1 + 0.1 + 0.02). So, the missing probability for Yellow is 1 - 0.8 = 0.2. Similarly, for the Peanut M&M table, the sum of the given probabilities is 0.72 (0.2 + 0.3 + 0.1 + 0.1 + 0.01). So, the missing probability for Yellow is 1 - 0.72 = 0.28.
a) To find the probability that a plain M&M is red or blue, you can simply add the probabilities of red (0.02) and blue (0.1), which gives 0.02 + 0.1 = 0.12.
b) To find the probability that a peanut M&M is not brown, you can add the probabilities of blue (0.3) and yellow (0.01), which gives 0.3 + 0.01 = 0.31.
For question 2:
To calculate the probabilities of the events, you can use the given information and the principles of probability.
a) P(S) - This is the probability that the selected room is a science room. Since there are 10 science rooms out of the total 25 rooms in the new wing, the probability is 10/25.
b) P(M or E) - This is the probability that the selected room is either a math room or an English room. There are 5 math rooms + 10 English rooms = 15 rooms that satisfy this condition, out of the total 25 rooms. So, the probability is 15/25.
c) P(E or B) - This is the probability that the selected room is either an English room or a biology room. There are 10 English rooms + 8 biology rooms = 18 rooms that satisfy this condition, out of the total 25 rooms. So, the probability is 18/25.
d) P(S and not C) - This is the probability that the selected room is a science room but not a chemistry room. There are 10 science rooms - 2 chemistry rooms = 8 rooms that satisfy this condition, out of the total 25 rooms. So, the probability is 8/25.
For question 3:
a) Given that the probability of dying from heart disease is 0.45 and the probability of dying from cancer is 0.22, to find the probability that a death was due to either heart disease or cancer, you can simply add the probabilities together: 0.45 + 0.22 = 0.67, or 67%.
b) To find the probability that a death was due to some other cause, you can subtract the probability of dying from heart disease or cancer (0.67) from 1 (since 100% represents all possibilities): 1 - 0.67 = 0.33, or 33%.