Calculating Probabilities of Independent and Dependent Events

This video tutorial explains the concepts of independent and dependent events in probability. Independent events are those where the occurrence of one event does not affect the probability of another, exemplified by rolling a die and flipping a coin. Dependent events, on the other hand, are where one event affects the probability of another, such as drawing marbles without replacement. The video provides examples and calculations for both types of events, emphasizing the correct formulas to use in each scenario.

What does it mean when two events are considered independent in probability?

• Both events must occur at the same time.

• The outcome of one event has no impact on the outcome of the other event.

• Both events must have the same probability of occurring.

• The outcome of one event affects the outcome of the other event.

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

• Add the probabilities of both events.

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

• Multiply the probabilities of both events.

• Subtract the probabilities of both events.

What is the probability of rolling a 5 on a 6-sided die and flipping heads on a coin?

• 1/6

• 1/12

• 1/3

• 1/2

What defines dependent events in probability?

• Events that can occur simultaneously without affecting each other.

• Events where the outcome of one does not affect the outcome of the other.

• Events where the outcome of one event affects the probability of the other occurring.

• Events that have equal probabilities of occurring.

In the context of drawing marbles from a box, what does 'without replacement' imply?

• All marbles are replaced with new ones after a draw.

• The marble is put back into the box after being drawn.

• The color of the marble does not affect the draw.

• The marble drawn is kept out of the box, affecting subsequent draws.

What is the probability of drawing a green marble followed by a blue marble from a box containing 7 green and 3 blue marbles, without replacement?

• 7/10

• 3/20

• 7/30

• 21/90

Why can't the multiplication rule for independent events be used for dependent events?

• Because dependent events cannot occur together.

• Because the outcomes of dependent events are always known.

• Because dependent events have a higher probability of occurring.

• Because the outcome of one event affects the outcome of the other.

What adjustment is made to the probability calculation formula for dependent events?

• No adjustment is needed; the same formula is used.

• The probabilities are added instead of multiplied.

• The probability of the second event is adjusted based on the outcome of the first.

• The probabilities are divided instead of multiplied.

What is the probability of drawing two green marbles in succession without replacement from a box with 7 green and 3 blue marbles?

• 21/30

• 6/19

• 7/15

• 42/90

How does the probability of drawing a blue marble change after drawing a green marble first without replacement from a box of 10 marbles?

• Decreases from 3/9 to 3/10

• Increases from 3/10 to 3/9

• Decreases from 1/2 to 1/3

• Remains the same at 3/10