Question

Pick two of the following topics and tell me what
you know about that topic. Give an example as supporting evidence. You may need more white
space than I gave you.
a) Random vs Simple Random sampling

b) Levels of Measurement

c) Conditional Probability

d) The Addition and Multiplication rules of Probability

Answer 1

C)

• conditional probability is a measure of the probability of an event occurring given that another event has occurred
• the probability of A under the condition B", is usually written as P(A | B)
• Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event

In a group of 100 sports car buyers, 40 bought alarm systems, 30 purchased bucket seats, and 20 purchased an alarm system and bucket seats. If a car buyer chosen at random bought an alarm system, what is the probability they also bought bucket seats?

Figure out P(A). It’s given in the question as 40%, or 0.4.

Figure out P(A∩B). This is the intersection of A and B: both happening together. It’s given in the question 20 out of 100 buyers, or 0.2.

Insert your answers into the formula:

P(B|A) = P(A∩B) / P(A) = 0.2 / 0.4 = 0.5.

The probability that a buyer bought bucket seats, given that they purchased an alarm system, is 50%.

D)

Addition rule of probability

• The addition rule states the probability of two events is the sum of the probability that either will happen minus the probability that both will happen
• The addition rule is: P(A or B) = P(A) + P(B) - P(A and B)

consider a class in which there are 9 boys and 11 girls. At the end of the term, 5 girls and 4 boys receive a grade of B. If a student is selected by chance, what are the odds that the student will be either a girl or a B student? Since the chances of selecting a girl are 11 in 20, the chances of selecting a B student are 9 in 20 and the chances of selecting a girl who is a B student are 5/20, the chances of picking a girl or a B student are:

11/20 + 9/20 - 5/20 =15/20 = ¾

Multiplication rule of probability

• If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is:

• P(A and B)=P(A)⋅P(B)

For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/2