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Intro to Probability

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Intro to Probability

Notes 15

Probability

- Probability – a number from 0 – 1 that represents the likelihood an event will happen. Can also be written as a percent.
- Helps us to make inferences and predict the outcome of an event in order to make informed decisions.

Probability Outcomes

½

0

1

Equally likely to occur

Impossible to occur

Certain to occur

50 %

0%

100%

Theoretical vs. Experimental

- Theoretical probability – each outcome has an equally likely chance of happening. It is what should occur.
- Experimental probability – probability calculated using data collected in an experiment. It is what actually occurs when an experiment is repeated many times.

Finding Probability

- The formula for probability is:
- “Or” → add each probability together
- “And” → multiply each probability together

Example 1 cont.

Calculate each probability using the spinner.

P(black and then green)

P(blue and then green or red)

Example 3

Kate has 3 jeans (light, medium, dark), 4 shirts (pink, blue, purple, white) and 2 pairs of shoes (converse and boots).

How many outfits are possible?

Find P(light or dark, white or pink, converse)

Example 4

A deli has 4 kinds of bread, 5 kinds of meat, and 3 kinds of cheese.

How many different sandwiches are possible with one bread, meat, and cheese?

Independent vs. Dependent

- Independent events: the occurrence of one event has no effect on the occurrence of the other event.
- Dependent events: the occurrence of one event affects the occurrence of the other event.

Independent vs. Dependent

- Consider choosing objects from a group of objects. If you replace the object each time, choosing additional objects are independent events.
- If you do not replace the object each time, choosing additional objects are dependent events.

Independent vs. Dependent

- Determine whether the events are independent or dependent:
- One coin is tossed, and then a second coin is tossed.
- Wednesday’s lottery numbers and Saturday’s lottery numbers.
- Andrea selects a shirt from her closet to wear on Monday and then a different shirt to wear on Tuesday.

Probability of 2 Independent Events

- If two events A and B are independent, then
P(A and B) = P(A) * P(B)

Example 5

- A coin is tossed and a die is rolled. What is the probability that the coin lands heads up and the number rolled is a 6?

Example 6

- Suppose you toss a coin four times. What is the probability of getting four tails?

Probability of 2 Dependent Events

- If two events A and B are dependent, then
P(A and B) = P(A) * P(B|A)

P(B|A): probability that event B occurs given A has already occurred

Example 7

- In a bag is 3 green and 4 blue marbles, a blue marble is drawn and not replaced. Then a second blue marble is drawn. Find the probability of this outcome: