Probability Concepts and Calculations

What is the key difference between independent and dependent events in probability?

• Independent events affect each other's outcomes.

• Dependent events are always mutually exclusive.

• Dependent events do not affect each other's outcomes.

• Independent events do not affect each other's outcomes.

If you flip a coin and roll a die, what is the probability of getting a head and a three?

• 1/2

• 1/12

• 1/3

• 1/6

In a deck of 52 cards, what is the probability of drawing a jack and then an eight with replacement?

• 1/13

• 1/52

• 1/169

• 1/26

What does 'replacement' mean in the context of probability events?

• The first event affects the second event.

• The first event does not affect the second event.

• The events are mutually exclusive.

• The total number of outcomes changes.

How does the probability calculation change when events are dependent?

• You add the probabilities of each event.

• You subtract the probability of the first event from the second.

• You multiply the probability of the first event by the conditional probability of the second.

• You multiply the probabilities of each event.

In a jar with marbles, what is the probability of drawing a green and then a yellow marble without replacement?

• 1/8

• 1/16

• 1/24

• 1/32

What is the probability of selecting two male fish in a row from a tank without replacement?

• 1/10

• 1/3

• 1/5

• 1/9

How can you determine if two events are independent using probability formulas?

• By checking if the sum of probabilities equals 1.

• By checking if the product of probabilities equals the intersection probability.

• By checking if the probabilities are mutually exclusive.

• By checking if the probabilities are equal.

If 60% of students are female and 50% have long hair, what is the probability that a student is both female and has long hair?

• 0.5

• 0.45

• 0.3

• 0.6

What conclusion can be drawn if the calculated intersection probability does not match the product of individual probabilities?

• The events are mutually exclusive.

• The events are equally likely.

• The events are dependent.

• The events are independent.