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.

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Probability
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
Probability Outcomes

½

0

1

Equally likely to occur

Impossible to occur

Certain to occur

50 %

0%

100%


Theoretical vs experimental
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
Finding Probability

  • The formula for probability is:

  • “Or” → add each probability together

  • “And” → multiply each probability together


Example 1
Example 1

Calculate each probability using the spinner.

P(red)

P(green or blue)


Example 1 cont
Example 1 cont.

Calculate each probability using the spinner.

P(black and then green)

P(blue and then green or red)


Counting
Counting

How many possible outcomes are there?

Tossing 4 coins?

Rolling 3 dice?


Example 2
Example 2

Three coins are tossed.

How many possible outcomes?

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


Example 3
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
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 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 dependent1
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 dependent2
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
Probability of 2 Independent Events

  • If two events A and B are independent, then

    P(A and B) = P(A) * P(B)


Example 5
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
Example 6

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


Probability of 2 dependent events
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
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
Assignment

Counting – Probability WS

Missed the Test?

See Mrs. James today!

Math’s Mate 3-2


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