Probability and Combinatorics Problems

Front

What is the formula for combinations?

Back

C(n, r) = n! / (r!(n - r)!) where n is the total number of items, r is the number of items to choose.

Front

How many ways can you choose 6 numbers from a set of 54?

Back

25,827,165 (using the combination formula C(54, 6)).

Front

What does P(A or B) represent in probability?

Back

The probability that either event A occurs, event B occurs, or both occur.

Front

If events A and B are mutually exclusive, how do you calculate P(A or B)?

Back

P(A or B) = P(A) + P(B).

Front

What is the formula for permutations?

Back

P(n, r) = n! / (n - r)! where n is the total number of items, r is the number of items to arrange.

Front

Calculate 8P4.

Back

1680 (using the permutation formula P(8, 4)).

Front

What is the probability of rolling a '4' exactly 25 times in 100 rolls of a fair die?

Back

1.0% (calculated using the binomial probability formula).

Front

Define mutually exclusive events in probability.

Back

Events that cannot occur at the same time; the occurrence of one event excludes the occurrence of the other.

Front

What is the total number of combinations for a lock with 40 numbers using 3 numbers without repetition?

Back

59280 (calculated using the permutation formula 40P3).

Front

What is the probability of an event that is certain to happen?

Back

1 (or 100%).