independent event & Mutually Exclusive

Front

What is an independent event in probability?

Back

An independent event is an event whose outcome does not affect the outcome of another event. For example, flipping a coin and rolling a die are independent events.

Front

How do you determine if two events A and B are independent?

Back

Two events A and B are independent if P(A and B) = P(A) * P(B).

Front

What does it mean for two events to be mutually exclusive?

Back

Two events are mutually exclusive if they cannot occur at the same time. For example, rolling a 2 and rolling a 5 on a single die are mutually exclusive events.

Front

If P(A) = 0.1 and P(B) = 0.3, what is P(A and B) if A and B are independent?

Back

P(A and B) = P(A) * P(B) = 0.1 * 0.3 = 0.03.

Front

True or False: If P(A) + P(B) < P(A or B), then A and B are not mutually exclusive.

Back

True.

Front

What is the probability of drawing an even number from a set of cards numbered 1-10?

Back

There are 5 even numbers (2, 4, 6, 8, 10) out of 10 cards, so the probability is 5/10 or 1/2.

Front

When rolling a die, what are the outcomes of rolling an even number and rolling a 5?

Back

These events are mutually exclusive because you cannot roll an even number and a 5 at the same time.

Front

What is the formula for calculating the probability of two independent events A and B occurring?

Back

P(A and B) = P(A) * P(B).

Front

If two events are not mutually exclusive, what does that imply about their probabilities?

Back

It implies that the events can occur at the same time, and P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the probability of drawing a card with a number greater than or equal to 5 from a set of cards numbered 1-10?

Back

There are 6 cards (5, 6, 7, 8, 9, 10) that are greater than or equal to 5, so the probability is 6/10 or 3/5.