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Intro to Probability

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Intro to Probability

Notes 15

- 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.

½

0

1

Equally likely to occur

Impossible to occur

Certain to occur

50 %

0%

100%

- 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.

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

Calculate each probability using the spinner.

P(red)

P(green or blue)

Calculate each probability using the spinner.

P(black and then green)

P(blue and then green or red)

How many possible outcomes are there?

Tossing 4 coins?

Rolling 3 dice?

Three coins are tossed.

How many possible outcomes?

Find P(HTH)Find P(all same side)

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)

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 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.

- 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.

- 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.

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

- 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?

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

- 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

- 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:

Counting – Probability WS

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Math’s Mate 3-2