I dont understand this topic very well. Can someone show me how to solve these p
ID: 3022384 • Letter: I
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I dont understand this topic very well. Can someone show me how to solve these problems with good explanations thats how I learn? Please do dont skip any step otherwise I get lost. please answer all questions and post the solutions. I would really apprecite it. Thank you so much!
3. With your eyes closed, you draw 2 M&Ms; without replacement from a bowl containing 10 orange, 15 green, 20 blue, and 25 yellow candies. You win S20 if you get two oranges, S15 if you get one each of orange and green, and $10 if you get one each of orange and blue. (a) What is the probability that you win S20? (b) What is the probability that you win $15? (c) Given that the first M&M; you draw is yellow, what is the probability that the second one you draw is green! (d) Given that you win S15, what is the probability that the first M&M; you draw is green? Thinking: Find the probability without doing any calculation (e) Thinking: Conditioned on the event that you win money, what is the probability that your first M&M; is orange? 4. Forecasters get predictions of tomorrow's Washington D.C. weather from the American model and the European model. (These are the two leading computer models). For simplic- ity, suppose that each model predicts either rain or no rain. If the American model predicts rain, there is rain the next day with probability .85. If the American model predicts no rain, there is no rain the next day with probability 0.9. The corresponding values for the European model are 0.9 and 0.92 (a) It What additional information do you need to calculate the probability that the Amer- ican model predicted rain yesterday, given that it rained today? (b) Thinking: It might be true that a forecaster should just use the European model. But it might be true that a forecaster should use both models. Explain in detail by inventing numerical examples consistent with the data already given.Explanation / Answer
a.) You will win $20 in 2 draws if you choose an orange M&M first and then one blue M&M or you choose one blue and then an orange M&M.
From the 70 candies there are 20 blue candies and you have to choose one of the them. Now there are 69 candies left and you have to choose 1 orange from the 10 oranges. Or
You can 1st choose one of the 10 orange candies from the 70 candies and the other candy can be chosen from one of the 20 blue candies of the 69 remaining candies
Probability = (20/70)(10/69) + (10/70)(20/69)
= 0.0828
b.) You ccan win $15 if you chose either one orange and one green or one green and one orange.
Probability = (10/70)(15/69) + (15/70)(10/69)
= 0.06211
c.) P(second is a green candy | first candy is yellow)
= P( selecting 1st yellow candy and then green)
= (25/70)(15/69)
= 0.0776
d.) From the 70 candied you can choose one of the 15 green candies in 15 ways
Therefore the probability will be 15/70
4.) You need the probability that it rained yesterday.
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