Goal: TLW apply Venn diagrams to probability. 3.9 Goal: TLW apply Venn diagrams to probability.

Venn Diagrams Helps simplify complicated probability problems.

Example Year 12 at an IB school has 38 candidates. One candidate anticipated mathematics and is not taking the subject in Year 12. Of the other 37 candidates: 17 take math studies 14 take math SL 6 take math HL A Year 12 candidate is picked at random. Find the probability that this candidate takes math studies.

Example In an IB school that total number of candidates taking DP: Math studies is 22 German is 16 French is 21 Of these: 2 are taking all three subjects 9 are taking math studies and French but not German 7 are taking math studies and German but not French 6 are taking German only Create a Venn diagram Fill in the entire diagram What’s the probability of: Taking just one of the subject German or math studies If the candidate does do German, what is the probability that s/he also takes math studies?

Tree Diagrams Use to represent alternate events and their probabilities. Flipping a Coin 1 2 H T

Flipping a coin twice. What’s the probability of heads and tails regardless of the order.

Example The probability that Jasmine wakes up by 7:30 am is 0.6. If Jasmine wakes up by 7:30, then the probability that she will catch the bus is 0.9. If she sleeps later than 7:30, the probability that she will catch the bus is 0.4. Draw a tree diagram representing the situation. Calculate the probability that Jasmine will catch the bus on any one day. If Jasmine goes to school 280 days in the year, how many of these days will Jasmine catch the bus?

Replacement and without replacement When you replace the sample size doesn’t change If you don’t replace the sample size grows smaller.

Example We have a box of shoes. There are 2 red, 6 blue and 4 white shoes. We will pick a shoe at random and replace it and pick again. Make a tree diagram to represent the stages of probability.

Example Continued We have a box of shoes. There are 2 red, 6 blue and 4 white shoes. We will pick a shoe at random and do no replace it and pick again. What’s the probability of ending up with 2 red shoes? A pair of matching shoes. Shoes are different colors.

Assignment P. 157 #1-4