Exploring Independent and Dependent Probability

What defines an independent event in probability?

• An event that always results in the same outcome.

• An event that is influenced by the outcome of another event.

• An event where the outcome is not affected by other events.

• An event that cannot occur simultaneously with another event.

If you roll a die three times, what type of events are these rolls considered?

• Independent events

• Mutually exclusive events

• Dependent events

• Sequential events

If a bag contains red and yellow marbles, and one is selected and then replaced before selecting another, what type of event is this?

• Mutually exclusive event

• Independent event

• Dependent event

• Complementary event

What is an example of a dependent event?

• Rolling a die and flipping a coin.

• Drawing a card from a deck and not replacing it before drawing another.

• Tossing two coins simultaneously.

• Spinning a spinner twice.

In a scenario where a marble is drawn from a bag, not replaced, and then another marble is drawn, what type of events are these?

• Mutually exclusive events

• Independent events

• Dependent events

• Complementary events

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

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

• Subtract the probability of one event from the probability of the other.

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

• Add the probabilities of each event.

What is the probability of selecting a vowel and then landing on blue in a game involving letter tiles and a spinner?

• 1/8

• 1/4

• 1/6

• 1/12

What changes in the probability calculation for dependent events compared to independent events?

• There is no change in how probabilities are calculated.

• The probabilities are added instead of multiplied.

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

• The probabilities are divided instead of multiplied.

When a sock is selected from a drawer and not replaced before selecting another, what does this exemplify?

• Independent selection

• Dependent selection

• Random selection

• Uniform selection

How does removing a piece of fruit from a basket after selecting it affect subsequent selections?

• It makes subsequent selections independent.

• It does not affect the probability of subsequent selections.

• It increases the probability of selecting the same type of fruit.

• It makes subsequent selections dependent.