Mutually Exclusive and Overlapping Events

Front

What are mutually exclusive events?

Back

Events that cannot occur at the same time. For example, rolling a 1 and rolling a 2 on a die.

Front

What are overlapping events?

Back

Events that can occur at the same time. For example, drawing a card that is both a heart and a red card.

Front

How do you calculate the probability of mutually exclusive events?

Back

P(A or B) = P(A) + P(B).

Front

How do you calculate the probability of overlapping events?

Back

P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the probability of not choosing a red rose from a vase with 12 red, 5 yellow, and 3 white roses?

Back

P(not red) = \frac{8}{20}.

Front

If the probability of rolling an odd number on a die is 0.5, what is the probability of rolling an even number?

Back

P(even) = 1 - P(odd) = 0.5.

Front

What is the probability of rolling a multiple of 2 or a multiple of 3 on a die?

Back

P(multiple of 2 or multiple of 3) = P(multiple of 2) + P(multiple of 3) - P(multiple of 6) = \frac{3}{6} + \frac{2}{6} - \frac{1}{6} = \frac{4}{6}.

Front

What is the total number of outcomes when rolling a six-sided die?

Back

6 outcomes: {1, 2, 3, 4, 5, 6}.

Front

What is the probability of getting heads if the probability of getting tails is 0.4?

Back

P(heads) = 1 - P(tails) = 0.6.

Front

What is the formula for calculating the probability of an event?

Back

P(event) = \frac{number \ of \ favorable \ outcomes}{total \ number \ of \ outcomes}.