Intro to Probability

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# Intro to Probability - PowerPoint PPT Presentation

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.

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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

Calculate each probability using the spinner.

P(red)

P(green or blue)

Example 1 cont.

Calculate each probability using the spinner.

P(black and then green)

P(blue and then green or red)

Counting

How many possible outcomes are there?

Tossing 4 coins?

Rolling 3 dice?

Example 2

Three coins are tossed.

How many possible outcomes?

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

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:
Assignment

Counting – Probability WS

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Math’s Mate 3-2