U7B Test Review

Front

How many ways can a president, vice president, and secretary be elected from 125 juniors?

Back

The number of ways to elect a president, vice president, and secretary from 125 juniors is calculated using permutations: P(125, 3) = 125! / (125-3)! = 125 * 124 * 123 = 1906500.

Front

What is the probability of both you and your best friend being chosen from 18 students?

Back

The probability of both you and your best friend being chosen is calculated as: P(both chosen) = (2/18) * (1/17) = 1/153.

Front

How many 2-digit numbers can be formed using the digits 1, 2, 3, and 4 without repeating digits?

Back

The number of 2-digit numbers is calculated as: 4 choices for the first digit and 3 choices for the second digit = 4 * 3 = 12.

Front

How to calculate the expected profit for a car dealer selling hybrids?

Back

Expected profit = Selling price - Cost price = $24,500 - $21,000 = $3,500 per car. If he sells 1,530 cars a week, expected weekly profit = 1,530 * $3,500 = $5,355.

Front

How many ways can you listen to 3 songs from a CD with 12 selections?

Back

The number of ways to choose 3 songs from 12 is calculated using combinations: C(12, 3) = 12! / (3!(12-3)!) = 220. However, since the order matters, we use permutations: P(12, 3) = 12 * 11 * 10 = 1320.

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by P(n, r) = n! / (n-r)!.

Front

What is a combination?

Back

A combination is a selection of objects without regard to the order. The number of combinations of n objects taken r at a time is given by C(n, r) = n! / (r!(n-r)!).

Front

Define probability in a mathematical context.

Back

Probability is a measure of the likelihood that an event will occur, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

What is the formula for calculating expected value?

Back

Expected value (EV) is calculated as EV = Σ (probability of outcome * value of outcome).

Front

How do you calculate the total number of outcomes in a probability experiment?

Back

The total number of outcomes is calculated by multiplying the number of choices available at each stage of the experiment.