6.6 (Mutually Exclusive & Overlapping Events)

Front

What are mutually exclusive events?

Back

Mutually exclusive events are events that cannot occur at the same time. For example, when rolling a die, rolling a 2 and rolling a 5 are mutually exclusive.

Front

What are overlapping events?

Back

Overlapping events are events that can occur at the same time. For example, owning a dog and owning a cat are overlapping events if some people own both.

Front

When rolling a single die, are rolling an even number and rolling a ‘5’ mutually exclusive?

Back

True

Front

How do you calculate the probability of either event A or event B occurring?

Back

P(A or B) = P(A) + P(B) - P(A and B) for overlapping events.

Front

If 19% of the population owns dogs and 14% owns cats, what is the probability that a person owns a cat or a dog if 6% own both?

Back

P(cat or dog) = 19/100 + 14/100 - 6/100.

Front

What is the probability of selecting a green or red marble from a bag containing 9 green, 5 yellow, and 6 red marbles?

Back

P(green or red) = (9 + 6) / (9 + 5 + 6) = 15/20 = 3/4.

Front

When rolling a single die, are rolling an odd number and rolling a prime number mutually exclusive?

Back

False

Front

What is the formula for calculating the probability of mutually exclusive events?

Back

P(A or B) = P(A) + P(B) for mutually exclusive events.

Front

What is the probability of selecting a yellow marble from a bag containing 9 green, 5 yellow, and 6 red marbles?

Back

P(yellow) = 5 / (9 + 5 + 6) = 5/20 = 1/4.

Front

If two events are mutually exclusive, what is the probability of both events occurring?

Back

The probability of both events occurring is 0.