Independent vs Dependent Events

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other. For example, flipping a coin and rolling a die are independent events.

Dependent events are two or more events where the occurrence of one event affects the occurrence of the other. For example, drawing a card from a deck and not replacing it before drawing another card.

The probability of independent events A and B occurring together is P(A and B) = P(A) * P(B).

The probability of dependent events A and B occurring together is P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given that A has occurred.

The probability of landing on one section is 1/4 or 25%.

The probability of getting heads when flipping a coin is 1/2 or 50%.

The probability of rolling a 3 on a standard die is 1/6 or approximately 16.7%.

The probability of drawing an Ace from a standard deck of 52 cards is 4/52 or 1/13, which is approximately 7.7%.

If the first card drawn was an Ace, the probability of drawing a second Ace is 3/51, since there are now 51 cards left.

The probability of getting tails on two consecutive flips is (1/2) * (1/2) = 1/4 or 25%.