Conditional Probability and the Multiplication Rule (3.2)

True or false?

If two events are independent, the P(A|B) = P(B).

• True: the P(A|B) = P(B) because event B already happened and that's all that matters / no one cares about event A

• False: the P(A|B) = P(A) because whatever happened in the given B event does not matter to event A.

Classify the events as independent or dependent.

A ball is selected from a bin of balls numbered 1 through 10. It is replaced, and then a second ball is selected.

• independent events

• dependent events

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

True or false?

If two events are dependent, the P(A | B) = P(A∩B) / P(B)

• True: the probability of event A happening given B has already happened is where they overlap compared to just set B

• False: the probability of event A happening given B has already happened is just the probability of A because no one cares what happened in event B

If two events are independent, then  $P\left(A\ and\ B\right)=P\left(A\right)\times P\left(B\right)$  

• True

• False

Tags

CCSS.HSS.CP.B.8

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

Use the Multiplication Rule to find the probability.

A coin is tossed and a die rolled.

Find the probability of tossing a tail and then rolling a number greater than 2.

• 1/3

• 1/2

• 1/6

• 1/4

Tags

CCSS.HSS.CP.B.8

CCSS.HSS.CP.A.2

Worst President: In a sample of 1446 US voters, 188 said Nixon was the worst president since WWII. Three registered voters are selected at random. Find the probability that all 3 say Nixon is the worst president.

• 0.002

• 0.017

• 0.390

• 0.240

Tags

CCSS.HSS.CP.B.8

CCSS.HSS.CP.B.9

Lottery Tickets: 49% of US adults have purchase a state lottery ticket in the past year. Of these 49%, about 27.5% have an income less than $36,000/year.

Find the probability that a randomly selected adult has purchase a lottery ticket and has an income less than $36,000.

• 0.135

• 0.765

• 0.176

• 0.240

Tags

CCSS.HSS.CP.B.8

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6

Surviving Surgery: A doctor gives a patient a 85% chance of surviving bypass surgery after a heart attack. Find the probability that a patient will not survive bypass surgery to the hundredths place.

Find the probability of tossing a coin 4 times and getting 4 heads.

Type your answer as a decimal rounded to the thousandths place.

Find the probability of selecting an ace from a deck of 52 cards and then selecting a king without replacing the ace.

Type your answer as a decimal rounded to three decimal places (the thousandths place).