Probability: Mutually Exclusive 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, getting a 3 and getting a 5 are mutually exclusive events.

Front

If you roll one die, what is the probability of getting an odd number or a 4?

Back

The probability is \( \frac{2}{3} \) because there are 3 odd numbers (1, 3, 5) and 1 even number (4) out of 6 total outcomes.

Front

How do you calculate the probability of the union of two mutually exclusive events?

Back

For mutually exclusive events A and B, the probability of A or B is given by \( P(A \cup B) = P(A) + P(B) \).

Front

When rolling a single die, the events of rolling an even number and rolling a ‘5’ are...

Back

Mutually Exclusive.

Front

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

Back

The probability is \( \frac{8}{20} \) or \( \frac{2}{5} \) because there are 8 non-red roses out of 20 total.

Front

What is the formula for calculating the probability of event A or event B?

Back

The formula is \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \). If A and B are mutually exclusive, then \( P(A \cap B) = 0 \).

Front

What does it mean if two events are overlapping?

Back

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

Front

If the probability of event A is \( \frac{1}{4} \) and the probability of event B is \( \frac{1}{3} \), what is the probability of A or B if they are mutually exclusive?

Back

The probability is \( P(A \cup B) = \frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12} \).

Front

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

Back

The total number of outcomes when rolling a die is 6.

Front

What is the probability of rolling a number less than 3 on a die?

Back

The probability is \( \frac{2}{6} = \frac{1}{3} \) because the numbers less than 3 are 1 and 2.