Compound Probability Continued AndOr Probability Pracitce Bellwork 1

Compound Probability Continued And/Or Probability Pracitce

Bellwork 1) Jane and Mark are making cookies for their moms. They have 12 chocolate chip, 5 sugar cookies, and 2 almond cookies. If they were to randomly grab a cookie to give to their moms, what is the chances of… a. b. c. d. P(Chocolate chip or almond): P(Almond): P(Not sugar cookie): P(Sugar and chocolate chip): 2) Diane has a bag of marbles. There are 12 red, 4 green, 3 blue, 1 yellow. She randomly reaches her hand into the bag and pulls out a marble. What is the probability it is a green or blue? a. Diane reaches into the bag and pulls out a blue marble and decides to set it aside. What is the new probability of pulling out a green marble? A red or yellow?

Learning Objectives By the end of this lecture, you should be able to: • Determine whether a problem is asking for independent or dependent probability • Apply the multiplication or addition rules to a probability situation • Describe what type of probability is taking place (and/or, independent/dependent) and solve

Just a reminder • Compound probability: The probability of MORE than one event taking place • Independent probability: when the probability of one event occurring DOES NOT affect the probability of another event occurring (This will always be OR probability) • Dependent probability: the outcome or occurrence of the first event DOES affect the outcome or occurrence of the second. (This will always be AND probability)

Example 2: If rolling a single die, determine the probability of rolling an odd number or number greater than 5.

More examples: • An automobile dealer decides to select a month for its annual sale. Find the probability that it will be September or October. • A bag contains 8 white marbles, 4 green marbles and 3 blue marbles. 2 marbles are selected at random without replacement, find the following probabilities: a) P(both are green) b) P(blue marble and white marble) c) P(white marble and green marble)

More examples: P(heart or circle): P(Square and circle): P(Not circle or a square): P(Not heart): P(Square)

Try this one out: • A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability that it is yellow or green? • If you roll a die, what is the probability of it being odd and less than 5? • Based off the picture to the right: • P(green or blue): • P(Not orange or green): • P(Orange and green):

• P(Green and heads): • P(Blue or purple): • P(Yellow and tails):

Try this out: • Mario has two new spinners to use to pick the vehicle he can use for work. One spinner is divided into equal sections and labeled: sedan, truck, van, and motorcycle. The other spinner has 3 equal parts for the colors: green, blue, and white. • P(white van): • P(blue truck): • P(Green Motorcycle):

What happens if there is overlap in the data? • When you are asked the probability of an event, specifically of a compound event, sometimes the data can overlap. • When this happens, you must take into account that you are only meant to count the probability of an event ONCE. • For example: • P(an even number or a number less than 3): • P(An odd number or a number divisible by 3):

Overlapping: If one or more events happen at the exact same time Mutually Exclusive: two events that CANNOT occur at the same time

Example 1: Example: What is the probability of randomly drawing either an ace or a heart from a deck of 52 playing cards?

General addition rule for any two events A or B: P(Event A) OR P(Event B) = P(A) + P(B) What is the probability of randomly drawing either an ace or a heart from a deck of 52 playing cards? Answer: There are 4 aces in the pack and 13 hearts. However, 1 card is both an ace and a heart. If you simply added the two probabilities separately, you would end up counting that same card twice. This is an example of overlapping. Thus: P(ace or heart) = P(ace) + P(heart) – P(ace and heart) = 4/52 (the 4 aces) + 13/52 (the 13 hearts) - 1/52 (the Ace of Hearts) = 16/52