Independent & Dependent Events

Independent events are events where the outcome of one event does not affect the outcome of another. For example, flipping a coin and rolling a die are independent events.

Dependent events are events where the outcome of one event affects the outcome of another. For example, drawing two cards from a deck without replacement is a dependent event.

The probability is independent. If the probability of drawing a yellow marble is $$\frac{5}{45}$$ , then the probability of drawing two yellow marbles is $$\frac{5}{45} \times \frac{5}{45} = \frac{25}{2025} = \frac{1}{81}$$ .

The probability is independent. The probability of not choosing a white shoe each time is $$0.6$$ , so the probability of none being white is $$0.6^3 = 0.216$$ .

The probability is dependent. If one iPad is won, the total number of prizes decreases, affecting the probability of winning a basketball.

The probability is independent. The probability is calculated as $$\frac{1}{6} \times \frac{1}{2} \times \frac{1}{6} = \frac{1}{72}$$ .

The probability is independent. Each roll of the dice is independent, so the probability of rolling a 1 is $$\frac{1}{6}$$ .

Probability is a measure of the likelihood of an event occurring. For independent events, the probability of both events occurring is the product of their individual probabilities.

In dependent events, the probability of the second event is affected by the outcome of the first event. The probability is calculated by adjusting the total outcomes based on the first event.

The formula is: P(A and B) = P(A) * P(B), where A and B are independent events.