Probability Rules

Front

What is the probability of drawing a purple chip followed by a black chip from a jar containing 4 white chips, 5 purple chips, and 1 black chip?

Back

P(purple then black) = \frac{5}{10} \times \frac{1}{9} = \frac{1}{18}

Front

What is the probability of drawing a 5 or a diamond from a standard deck of cards?

Back

P(5 or diamond) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}

Front

Which rule should you use to find the probability of two events A and B occurring if P(A) = \frac{9}{10}?

Back

Use the Multiplication Rule.

Front

What is the probability of flipping a nickel three times and getting tails each time?

Back

P(tails, tails, tails) = \left(\frac{1}{2}\right)^3 = \frac{1}{8}

Front

What is the probability of rolling two number cubes and getting a sum of 7 or 4?

Back

P(sum = 7 or 4) = P(sum = 7) + P(sum = 4) = \frac{6}{36} + \frac{3}{36} = \frac{9}{36} = \frac{1}{4}

Front

Define the Multiplication Rule in probability.

Back

The Multiplication Rule states that the probability of two independent events A and B occurring together is P(A) \times P(B).

Front

What is the Complement Rule in probability?

Back

The Complement Rule states that the probability of an event not occurring is 1 minus the probability of the event occurring: P(A') = 1 - P(A).

Front

If you have a bag with 3 red, 2 blue, and 5 green marbles, what is the probability of drawing a blue marble?

Back

P(blue) = \frac{2}{10} = \frac{1}{5}.

Front

What is the probability of rolling a 3 on a single die?

Back

P(rolling a 3) = \frac{1}{6}.

Front

How do you calculate the probability of drawing two cards from a deck without replacement?

Back

P(A and B) = P(A) \times P(B|A), where P(B|A) is the probability of B given A has occurred.