Probability - Multiplication Rule

Front

What is the Multiplication Rule in probability?

Back

The Multiplication Rule states that the probability of two independent events occurring together is the product of their individual probabilities.

Front

If the probability of event A is 0.5 and the probability of event B is 0.3, what is the probability of both A and B occurring?

Back

Using the Multiplication Rule: P(A and B) = P(A) * P(B) = 0.5 * 0.3 = 0.15.

Front

What is the probability of selecting a yellow cube followed by a green cube from a bag containing 8 green, 6 red, and 14 yellow cubes?

Back

P(yellow then green) = P(yellow) * P(green | yellow) = \frac{14}{28} * \frac{8}{27} = \frac{4}{27}.

Front

How do you calculate the probability of selecting two items without replacement?

Back

Calculate the probability of the first item, then multiply by the probability of the second item given the first has been removed.

Front

What is the total number of outcomes when selecting one box from 20 boxes of cereal A and one from 10 boxes of cereal B?

Back

Total outcomes = 20 * 10 = 200.

Front

What is the probability that neither box has a prize if one box is selected from each type of cereal?

Back

P(neither has a prize) = P(no prize from A) * P(no prize from B) = \frac{19}{20} * \frac{9}{10} = \frac{171}{200}.

Front

If Nick selects a digit from {0, 1, 2, ..., 9} and a letter from {A, B, C, ..., Z}, what is the probability that he guesses both incorrectly?

Back

P(incorrect digit) = \frac{9}{10}, P(incorrect letter) = \frac{25}{26}. Therefore, P(both incorrect) = \frac{9}{10} * \frac{25}{26}.

Front

What is the probability of selecting a purple pencil and a black pen from a set of pencils and pens?

Back

P(purple pencil and black pen) = P(purple pencil) * P(black pen) = \frac{1}{6} * \frac{1}{3} = \frac{1}{18}.

Front

How do you express the probability of the third key unlocking the cabinet if there are 10 keys?

Back

P(third key is the correct one) = P(first two are incorrect) * P(third is correct) = \left(\frac{9}{10}\right) * \left(\frac{8}{9}\right) * \left(\frac{1}{8}\right).

Front

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

Back

For independent events A and B, P(A and B) = P(A) * P(B).