Multiplication Rule for Probability

Front

What is the Multiplication Rule for Probability?

Back

The Multiplication Rule states that the probability of two independent events occurring together is the product of their individual probabilities. For dependent events, the probability of the second event is affected by the first.

Front

If the probability of event A is P(A) and the probability of event B is P(B), what is the probability of both A and B occurring?

Back

For independent events: P(A and B) = P(A) * P(B). For dependent events: P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given A has occurred.

Front

How do you calculate the probability of drawing two marbles from a bag without replacement?

Back

Calculate the probability of drawing the first marble, then multiply it by the probability of drawing the second marble given the first has been drawn. For example, if there are 5 red and 3 blue marbles, the probability of drawing a red first and then a blue is: P(Red) * P(Blue|Red) = (5/8) * (3/7).

Front

What is the probability of selecting a white marble from a bag containing 12 red, 6 white, and 2 blue marbles?

Back

The probability of selecting a white marble is the number of white marbles divided by the total number of marbles: P(White) = 6/(12+6+2) = 6/20 = 3/10.

Front

In a key ring with 12 keys, 3 of which open a door, what is the probability that a randomly selected key does not open the door?

Back

The probability that a randomly selected key does not open the door is the number of keys that do not open the door divided by the total number of keys: P(Not Open) = (12-3)/12 = 9/12 = 3/4.

Front

What is the probability of selecting a news magazine first and then a sports magazine from a stack of 5 news and 10 sports magazines?

Back

The probability of selecting a news magazine first is 5/15. After selecting a news magazine, there are 14 magazines left, so the probability of selecting a sports magazine next is 10/14. Therefore, P(News then Sports) = (5/15) * (10/14) = 1/3 * 5/7 = 5/21.

Front

If a bag contains 20 boxes of cereal A and 10 boxes of cereal B, what is the probability that neither box selected has a prize?

Back

The probability that the first box does not have a prize is 29/30 (29 non-prize boxes out of 30 total). The probability that the second box also does not have a prize is 28/29. Therefore, P(Neither has a prize) = (29/30) * (28/29) = 28/30 = 14/15.

Front

What is the probability of drawing 3 white marbles from a bag containing 6 white marbles and 12 red marbles?

Back

The probability of drawing 3 white marbles without replacement is: P(1st White) = 6/18, P(2nd White|1st White) = 5/17, P(3rd White|2nd White) = 4/16. Therefore, P(3 Whites) = (6/18) * (5/17) * (4/16) = 1/51.

Front

What is the formula for calculating the probability of independent events?

Back

For independent events A and B, the probability of both events occurring is given by: P(A and B) = P(A) * P(B).

Front

How do you find the probability of selecting a specific key from a set of keys?

Back

The probability of selecting a specific key is the number of favorable outcomes (1 specific key) divided by the total number of outcomes (total keys). For example, if there are 10 keys, P(Specific Key) = 1/10.