Probability of Independent and Dependent Events

Front

What is the definition of independent events in probability?

Back

Independent events are two or more events where the occurrence of one event does not affect the probability of the other event occurring.

Front

What is the definition of dependent events in probability?

Back

Dependent events are two or more events where the occurrence of one event affects the probability of the other event occurring.

Front

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

Back

To calculate the probability of independent events occurring together, multiply the probabilities of each individual event: P(A and B) = P(A) * P(B).

Front

How do you calculate the probability of dependent events occurring together?

Back

To calculate the probability of dependent events occurring together, multiply the probability of the first event by the conditional probability of the second event given the first: P(A and B) = P(A) * P(B|A).

Front

What is the probability of selecting a lollipop from a bag containing 6 lollipops and 4 gum balls?

Back

The probability of selecting a lollipop is 6/(6+4) = 6/10 = 3/5.

Front

If a treat is selected and not replaced, how does it affect the probability of the next selection?

Back

If a treat is selected and not replaced, the total number of treats decreases, which affects the probability of the next selection, making it dependent on the first selection.

Front

What is the probability of selecting a yellow gummy bear from a bag containing 4 red, 5 green, and 3 yellow gummy bears?

Back

The probability of selecting a yellow gummy bear is 3/(4+5+3) = 3/12 = 1/4.

Front

What is the probability of selecting a red pen from a box containing 3 black pens, 7 blue pens, and 5 red pens?

Back

The probability of selecting a red pen is 5/(3+7+5) = 5/15 = 1/3.

Front

What is the combined probability of selecting a red pen and then a black pen without replacement?

Back

The combined probability is P(red) * P(black|red) = (5/15) * (3/14) = 15/210 = 1/14.

Front

What is the probability of selecting a gum ball first and then a lollipop from a bag containing 6 lollipops and 4 gum balls without replacement?

Back

The probability is P(gum ball) * P(lollipop|gum ball) = (4/10) * (6/9) = 24/90 = 4/15.