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# Applied 40S March 16, 2009

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Independent and dependent probabilities.

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### Applied 40S March 16, 2009

1. 1. RED and BLUE Marbles or ... all about dependant and independant events Biglie by ﬂickr user mat.teo
2. 2. A bag has 3 red and 5 blue marbles. Find P(RR), the probability of drawing 2 Red marbles) if the ﬁrst is replaced when chosen.
3. 3. A bag has 3 red and 5 blue marbles. Find P(RR) if the ﬁrst is not replaced when chosen.
4. 4. Dependent and Independent probabilities ... Independent Events Events in which the outcome of one event does not affect the outcome of the other event. Example A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and then replaced back in the bag. A second marble is selected, what is the probability that it is blue?
5. 5. Dependent and Independent probabilities ... Dependent Events If the outcome of one event affects the outcome of another event, then the events are said to be dependent events. Example A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and NOT replaced back in the bag. A second marble is selected, what is the probability that it is blue?
6. 6. Drag Examples: and Drop Which of the following are dependent events? Which are independent ? 1. Removing (selecting randomly) three red marbles without replacement from a bag that contains six red and nine blue dependent marbles. 2. Selecting a red card from a deck of cards, returning the card to the deck, shufﬂing the cards, and selecting a second red card. independent 3. Rolling two dice. independent 4. The weather and how likely you are to go visiting. You have decided that there is a 50% chance that you will visit your friend if it does not snow, and a 10% chance if it does snow. dependent
7. 7. Marbles A jar contains 5 red and 7 blue marbles. What is the probability of pulling out 2 blue marbles in a row, with replacement?
8. 8. Marbles (again) A jar contains 5 red and 7 blue marbles. What is the probability of pulling out 2 blue marbles in a row, without replacement?
9. 9. 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 2/3. The probability that he drinks cocoa is 1/5. If he drinks cocoa, the probability of him having pancakes is 6/7. HOMEWORK 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.
10. 10. Testing for independence ... 30% of seniors get the ﬂu every year. 50% of seniors get a ﬂu shot annually. 10% of seniors who get the ﬂu shot also get the ﬂu. Are getting a ﬂu shot and getting the ﬂu independent events? HOMEWORK P(shot) = 0.50 P(ﬂu) = 0.30 P(shot & ﬂu) = (0.50)(0.30) = 0.15 However P(shot & ﬂu) = 0.10
11. 11. The probability that Gallant Fox will win the ﬁrst race is 2/5 and that Nashau will win the second race is 1/3. HOMEWORK 1. What is the probability that both horses will win their respective races? 2. What is the probability that both horses will lose their respective races? 3. What is the probability that at least one horse will win a race?