Exploring the Multiplication Rule in Probability

What defines two events as independent?

• The outcome of one event does not influence the other.

• One event affects the outcome of the other.

• Both events must occur simultaneously.

• Both events have the same probability of occurring.

What is an example of independent events?

• Drawing two specific cards in sequence without replacement.

• Rolling a die and getting a 5 followed by rolling a 3.

• Picking two red balls consecutively from a bag without replacement.

• Flipping a coin and getting heads, then tails when using two different coins.

What changes the probability of drawing a queen after a king has been drawn without replacement?

• The number of cards increases.

• The probability of drawing a queen remains the same.

• The number of queens increases.

• The total number of cards decreases.

What is an example of dependent events?

• Choosing two marbles from separate bags.

• Flipping two coins simultaneously.

• Rolling different numbers on a die in two rolls.

• Drawing a card from a deck, not replacing it, then drawing another.

Why do dependent events affect each other's probabilities?

• Because the outcome of one changes the total outcomes for the other.

• Because they cannot occur at the same time.

• Because they always have the same outcome.

• Because they are always mutually exclusive.

What is the probability of rolling a 3 and then a 5 with a six-sided die?

• 2/36

• 1/18

• 1/36

• 1/12

How do you calculate the probability of two independent events occurring?

• Add the probabilities of each event.

• Divide the probability of one event by the other.

• Multiply the probability of one event by the probability of the other.

• Subtract the probabilities of each event.

What is the probability of drawing a king and then a queen from a deck of cards without replacement?

• 1/169

• 16/2652

• 4/52

• 8/2652

What rule is applied to calculate the probability of dependent events?

• Subtraction rule

• Division rule

• Addition rule

• General multiplication rule

What does the probability of B given A has already occurred signify?

• B's probability is independent of A.

• B's probability changes because A occurred.

• A and B are mutually exclusive events.

• A's probability is unaffected by B.