Chapter 5 Probability Practice Test

Front

What is the probability of the union of two events, Pizza and the complement of Water?

Back

The probability of the union of two events A and B is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B). In this case, P(Pizza ∪ Water^c) = 318/400.

Front

In a class of 30 students, if 20 do their homework regularly and 18 are passing, what is the probability that a randomly chosen student is not passing and not doing their homework?

Back

To find the probability of a student not passing and not doing homework, we can use the total number of students and the number of students who are not passing and not doing homework. The answer is 8/30.

Front

How do you calculate the conditional probability of an event?

Back

The conditional probability of event A given event B is calculated as P(A|B) = P(A ∩ B) / P(B). This is used to find the probability of A occurring given that B has occurred.

Front

What is the probability that a concert goer wore sandals given they wore pants?

Back

This is a conditional probability problem. The probability is given as 2/7.

Front

What is the probability that a randomly selected 60-year-old has a lung condition if 23% of adults smoke and 57% of smokers develop the condition?

Back

The probability that a randomly selected 60-year-old has the lung condition is 0.2312.

Front

Define the term 'complement' in probability.

Back

The complement of an event A, denoted A^c, is the event that A does not occur. The probability of the complement is P(A^c) = 1 - P(A).

Front

What is the formula for calculating the probability of independent events?

Back

For independent events A and B, the probability of both A and B occurring is P(A ∩ B) = P(A) * P(B).

Front

Explain the concept of mutually exclusive events.

Back

Two events are mutually exclusive if they cannot occur at the same time. For example, rolling a die cannot result in both a 2 and a 5 at the same time.

Front

What is Bayes' theorem in probability?

Back

Bayes' theorem relates the conditional and marginal probabilities of random events. It is expressed as P(A|B) = [P(B|A) * P(A)] / P(B).

Front

How do you find the probability of the intersection of two events?

Back

The probability of the intersection of two events A and B is given by P(A ∩ B) = P(A) + P(B) - P(A ∪ B).