4.7 to 4.9 Conditional Probability, Events & Union of Events

Multiple Choice

What are the two types of random variables discussed in this chapter?

• Discrete Random Variables

• Continuous Random Variables

• Both Discrete and Continuous

• Neither Discrete nor Continuous

Multiple Choice

What are the differences between discrete and continuous random variables?

• Discrete random variables can take on any value within a range.

• Continuous random variables can only take on specific values.

• Discrete random variables are countable, while continuous random variables are measurable.

• Both types of random variables are used in probability distributions.

Multiple Choice

Which of the following expressions correctly shows an expected value calculation for the probability distribution below?

• $$EV=\left(-5\cdot1\cdot8\right)+\left(0.4\cdot0.35\cdot0.25\right)$$

• $$EV=\left(-5+8+1\right)\cdot\left(0.4+0.35+0.25\right)$$

• $$EV=\left(-5\cdot0.4\right)+\left(1\cdot0.35\right)+\left(8\cdot0.25\right)$$

• $$EV=\left(-5\div0.4\right)+\left(1\div0.35\right)+\left(8\div0.25\right)$$

Multiple Choice

A discrete random variable X has the probability distributions shown in the table. Find the value of k. (Remember that a valid probability distribution must add up to 1)

• 1/3

• 7/12

• 1/12

• 1/4

Multiple Choice

What are the two requirements that the probabilities of a discrete random variable must satisfy?

• They must be between 0 and 1, and their sum must be 1

• They must be whole numbers, and their sum must be 100

• They must be less than 1, and their sum must be 0

• They must be greater than 0, and their sum must be 10

Multiple Choice

What is the probability of randomly choosing a healthy baby with an Apgar score of 7 or higher?

• 0.001

• 0.319

• 0.908

• 0.437

Multiple Choice

Find the mean (expected value) of the probability distribution.

• 85

• 83.2

• 87.1

• 84.4

Open Ended

Compute the mean of the random variable X and interpret it in context.

Multiple Choice

What is the formula for the variance of a discrete random variable X?

• Var(X) = Σ (xi - μX)² pi

• Var(X) = Σ (xi)² pi

• Var(X) = μX²

• Var(X) = Σ (xi - μX) pi

Multiple Choice

Compute the standard deviation of the random variable X and interpret it in context.

• 1.437

• 8.128

• 2.066

• 0.001

Multiple Choice

What is a continuous random variable?

• A variable that takes on all values in an interval of numbers

• A variable that can only take on discrete values

• A variable that is always positive

• A variable that is always negative

Multiple Choice

What is the probability that a randomly chosen young woman has height between 68 and 70 inches?

• 0.0562

• 0.9868

• 0.9306

• 0.5

Multiple Choice

What is a random variable?

• A variable that takes numerical values determined by the outcome of a chance process

• A fixed set of possible values with gaps between them

• A variable that takes all values in some interval of numbers

• A variable that describes the probability distribution of a continuous random variable

Multiple Choice

What is the expected value of a discrete random variable X?

• X = Σ Xi pi

• X = X1 p1 + X2 p2 + X3 p3

• X = average of all possible values

• X = variance of the random variable

Multiple Choice

The mean amount of time to mix the batter for a cake is 14 minutes with a standard deviation of 2.5 minutes. The mean amount of time to bake the cake is 35 minutes with a standard deviation of 6.2 minutes. What is the mean time to make and bake a cake? What is the standard deviation?

• mean = 49 min sd = 8.7 min

• mean = 49 min sd = 6.685 min

• mean = 21 min sd = 8.7 min

• mean = 21 min sd = 6.685 min

Draw

What is the probability of getting “heads” 5x in a row? Solve this problem first by drawing a tree diagram.

Open Ended

What is the probability of getting “heads” 5x in a row? Solve the problem without a tree diagram, with work.

Poll

How confident do you feel about this topic now?

• Very confident
• Somewhat confident
• Not confident