Conditional Probability

Front

What is Conditional Probability?

Back

The probability of an event occurring given that another event has already occurred.

Front

What is the formula for Conditional Probability?

Back

P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given B.

Front

Define Independent Events.

Back

Two events are independent if the occurrence of one does not affect the probability of the other.

Front

Define Dependent Events.

Back

Two events are dependent if the occurrence of one event affects the probability of the other.

Front

What is Theoretical Probability?

Back

Theoretical probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.

Front

How do you calculate the probability of drawing a red marble from a bag with 3 red, 2 blue, and 4 yellow marbles?

Back

P(red) = Number of red marbles / Total marbles = 3/9 = 1/3.

Front

What is the probability of selecting a woman who likes blue if the probability of a woman liking blue is 10% and the probability of being a woman is 40%?

Back

P(Woman|Likes Blue) = P(Woman and Likes Blue) / P(Likes Blue) = 0.1 / 0.4 = 0.25.

Front

How do you calculate the probability of drawing two purple marbles without replacement from a box of 5 purple, 3 green, and 2 orange marbles?

Back

P(both purple) = (5/10) * (4/9) = 20/90 = 2/9.

Front

What is the probability of drawing a white chip, then a purple chip, then a black chip from a jar containing 4 white, 5 purple, and 1 black chip?

Back

P(white, then purple, then black) = (4/10) * (5/9) * (1/8) = 20/720 = 1/36.

Front

What does it mean for events to be Conditional?

Back

Conditional events are those where the outcome of one event affects the outcome of another.