Compound Probability

Front

What is Compound Probability?

Back

Compound probability refers to the probability of two or more events happening at the same time. It can be calculated using the multiplication rule for independent events or the addition rule for mutually exclusive events.

Front

Define Independent Events in Probability.

Back

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other. For example, flipping a coin and rolling a die are independent events.

Front

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

Back

The probability of two independent events A and B occurring is given by: P(A and B) = P(A) * P(B).

Front

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

Back

The probability of two dependent events A and B occurring is given by: P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given that A has occurred.

Front

If a bag contains 3 red, 2 blue, and 5 green marbles, what is the probability of picking a red marble?

Back

The probability of picking a red marble is P(Red) = Number of Red Marbles / Total Marbles = 3 / (3 + 2 + 5) = 3/10.

Front

What is the probability of picking a blue marble followed by a green marble with replacement?

Back

P(Blue, Green) = P(Blue) * P(Green) = (2/10) * (5/10) = 1/10.

Front

What is the probability of picking a green marble followed by a red marble without replacement?

Back

P(Green, Red) = P(Green) * P(Red|Green) = (5/10) * (3/9) = 1/6.

Front

Explain the difference between 'with replacement' and 'without replacement' in probability.

Back

'With replacement' means that after an item is picked, it is put back into the set before the next pick, keeping the total number the same. 'Without replacement' means that once an item is picked, it is not returned, reducing the total number for the next pick.

Front

If the probability of an event A is 0.4, what is the probability of the event not occurring?

Back

The probability of event A not occurring is given by: P(Not A) = 1 - P(A) = 1 - 0.4 = 0.6.

Front

What is the probability of rolling a 3 on a fair six-sided die?

Back

The probability of rolling a 3 is P(3) = Number of favorable outcomes / Total outcomes = 1/6.