Conditional Probability

Conditional Probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which means the probability of event A occurring given that event B has occurred.

Conditional Probability is calculated using the formula: P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring.

P(A ∩ B) represents the probability that both events A and B occur simultaneously.

The Complement Rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. If P(A) is the probability of event A, then P(A') = 1 - P(A).

Using the Complement Rule, P(A') = 1 - P(A) = 1 - 0.3 = 0.7.

For independent events A and B, the probability of both events occurring is given by P(A ∩ B) = P(A) * P(B).

The total number of chips is 10. The probability of drawing a white chip is P(white) = 4/10 = 0.4.

After drawing a white chip, there are 9 chips left (3 white, 5 purple, 1 black). The probability of drawing a purple chip is P(purple|white) = 5/9.

If there are n cards, the probability of drawing card A first and card B second is P(A first, B second) = P(A) * P(B|A) = (1/n) * (1/(n-1)).

This is known as Conditional Probability and is denoted as P(A|B). It quantifies the likelihood of event A occurring under the condition that event B has already occurred.