Stats: Review Chapter 8 - Compound Probabilities

Front

What is the formula for calculating 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, and ! denotes factorial.

Front

How many ways can you choose 4 students from a class of 24?

Back

10,626 ways (C(24, 4) = 24! / (4!(24 - 4)!) = 10,626).

Front

What is a tree diagram in probability?

Back

A tree diagram is a visual representation of all possible outcomes of a probability experiment, showing the paths and their associated probabilities.

Front

How do you calculate the probability of two independent events occurring?

Back

P(A and B) = P(A) * P(B) for independent events A and B.

Front

What is the probability of selecting a yellow pencil and then a floral pencil without replacement?

Back

P(yellow ∩ floral) = (6/20) * (4/19) = 24/380 = 6/95.

Front

What does 'without replacement' mean in probability?

Back

'Without replacement' means that once an item is selected, it is not returned to the original set, affecting the probabilities of subsequent selections.

Front

What is the probability of selecting a vegetarian pizza with a cauliflower crust?

Back

P(vegetarian and cauliflower crust^C) = 2/9.

Front

How do you find the probability of a specific outcome in a sample space?

Back

P(outcome) = Number of favorable outcomes / Total number of outcomes in the sample space.

Front

What is the probability of selecting a queen and then a five from a deck of cards without replacement?

Back

P(queen ∩ five) = (4/52) * (4/51) = 16/2652 = 4/663.

Front

What is the significance of the probability 0.27 in the context of living to 100 years?

Back

It represents the likelihood that a randomly selected British woman born in 2003 will live to be at least 100 years old.