Probability...Con't

Probability...con't 1

Today the first thing we did was answer the following questions: Identify each of the following as experiments involving dependent in independent events. a. Toss and coin and roll and die six. INDEPENDENT This is an independent event because the outcome of rolling a die six does not depend on the coin being tossed, and vice‐versa. b. Draw 2 cards from a 52 card deck, without replacement. DEPENDENT This is a dependent event because you have no idea what kind of cards you took from the deck the first two times to guess what card you can get next. c. Draw 2 cards from a 52 card deck, with replacement. INDEPENDENT Because you replaced the cards you removed, the third time you take a card does not depend on the ones you picked before. 2

nd 2 Question: Two marbles are drawn. If the 1st marble is blue it is discarded and replaced with a red. Similarly, if the 1st marble is red it is discarded and replaced with a blue one. What is the probability that the second marble is blue? Step 1: Make a tree diagram Step 2: List the sample space Step 3: Complete the question 3

Solution: Step 1: Tree Diagram Step 2: Sample Space P(BB) = 1 1 = 1 B1 6 2 3 Notice how 3 P(BR) = 1 2 =2 when all are 2 3 6 added, the B1 P(RB) = 1 2 2 sum is equal = 2 2 3 6 to 1 1 1 1 P(RR) = R2 = 2 3 6 21 3 Step 3: Getting the Answer 33 To find the probability of having the B2 second marble blue, add the values 3 from the sample space above that have R1 blue (B) as the marble picked second. 2 2 1 P(2nd Marble Blue) = + 6 6 R1 1 = 3 2 4

rd 3 Question: Breakfast for Rupert Rupert has either milk or cocoa to drink for breakfast with either oatmeal or pancakes. If he drinks milk, then the probability that he is having pancakes with the milk is 2/5. The probability that he drinks cocoa is 1/4. If he drinks cocoa, the probability of him having pancakes is 3/8. a) Show the sample space of probabilities using a tree diagram or any other method of your choice. b) Find the probability that Rupert will have oatmeal with cocoa tomorrow morning. 5

Solution: P(MP) = 6 20 2. Because the sum A) P2 of the fractions has P(MO) = 9 to equal 1, we 5 20 conclude that the M3 probability Rupert P(CP) = 3 4 drinks milk is 3/4. 32 O3 3. The same rule P(CO) = 5 5 applies to these in 32 finding the P3 probabilities for The answer to (b) 8 pancakes and is .. P(CO) = 5 oatmeal C 1 32 4 1. The probability Since it is when he O5 Rupert will drink has cocoa and cocoa is 1/4 oatmeal together 8 6

rd 3 Question: The probability that Gallant Fox will win the first race is 2/5 and that Nashau will win the second race is 1/3. 1. What is the probability that both horses will win their respective races? Probability Gallant Fox will win 1= 2 2 multiplied by the probability 5 15 3 Nashau will win 7

2. What is the probability that both horses will lose their respective races? 1 ‐ P(Gallant Fox wins) = P(Gallant Fox loses) 1 ‐2 = 3 55 1 ‐ P(Nashau wins) = P(Nashau loses) P(Both Lose) = 2 3 35 1= 1‐ 2 6 3 = or 5 15 3. What is the probability that at least one horse will win a race? 1 ‐ P(Both lose) = P(at least one win) 1‐ 2 = 3 5 5 8

Probability...Con't

by JessiccaI on Jan 10, 2008

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Probability...Con’t — Presentation Transcript