The Multiplication Rules and Conditional Probability

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. If A and B are independent events, then P(A and B) = P(A) * P(B).

Front

Define conditional probability.

Back

Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which means the probability of A given B.

Front

What is the formula for conditional probability?

Back

The formula for conditional probability is P(A|B) = P(A and B) / P(B), provided that P(B) > 0.

Front

If a box contains 20 boxes of cereal A and 10 boxes of cereal B, what is the probability of selecting a box of cereal A?

Back

The probability of selecting a box of cereal A is P(A) = Number of A boxes / Total boxes = 20 / (20 + 10) = 20 / 30 = 2/3.

Front

What is the probability of selecting a box of cereal B?

Back

The probability of selecting a box of cereal B is P(B) = Number of B boxes / Total boxes = 10 / (20 + 10) = 10 / 30 = 1/3.

Front

How do you calculate the probability of neither event occurring?

Back

To calculate the probability of neither event A nor event B occurring, use the formula: P(neither A nor B) = 1 - P(A) - P(B) + P(A and B).

Front

What is the probability of selecting two keys that do not open the door from a key ring with 12 keys, 3 of which open the door?

Back

The probability is P(neither key opens the door) = (9/12) * (8/11) = 72/132 = 6/11.

Front

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

Back

The probability is P(news first, then sports) = (5/15) * (10/14) = 50/210 = 5/21.

Front

What is the total number of outcomes when spinning two spinners?

Back

If each spinner has n sections, the total number of outcomes when spinning both is n * n = n^2.

Front

If two spinners each have 6 sections, what is the probability that they land on numbers that sum to 3.5?

Back

The probability is P(sum = 3.5) = 1/24, assuming the only combination that sums to 3.5 is valid.