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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

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Math’s Mate 3-2