MAT 3772 Homework 1 Prof. Boyan Kostadinov 9/15/2017 Conditional Probability, Co
ID: 3304728 • Letter: M
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MAT 3772 Homework 1 Prof. Boyan Kostadinov 9/15/2017 Conditional Probability, Computing Probability by Conditioning I. In a standard deck of cards, the probability that the suit of a random card is hearts is 13/52-1/4 Assume that a standard deck has one card missing. A card is picked from the deck. Find the probability that it is a heart. Answer: 1/4 2. A regional insurance company insures homeowners against flood damage. Half of their policyholders are in Florida, 30% in Louisiana, and 20% in Texas. Company actuaries give the following estimates for the probability that a policyholder will file a claim for flood damage over the next year: 0.03 for Florida; 0.015 for Louisiana; 0.02 for Texas .(a) Find the probability that a random policyholder will file a claim for flood damage next year .(b) A claim was filed. Find the probability that the policyholder is from Texas. 3. Bob has n coins in his pocket. One is two-headed, the rest are fair. A coin is picked at random, lipped, and shows heads. Find the probability that the coin is two-headed. 4. (popular job-interview problem) A rat is trapped in a maze with three doors and some hidden cheese. If the rat takes door one, he will wander around the maze for 2 minutes and return to where he started. If he takes door two, he will wander around the maze for 3 minutes and return to where he started. If he takes door three, he ll find the cheese after 1 minute. If the rat returns to where he started he immediately picks a door to pass through. The rat picks each door uniformly at random How long, on average, will the rat wander before finding the cheese?Explanation / Answer
Ans:
2)Given that
P(Florida)=0.5
P(Lousiana)=0.3
P(Texas)=0.2
P(claim/Florida)=0.03
P(claim/Lousiana)=0.015
P(claim/Texas)=0.02
a)P(claim)=0.5*0.03+0.3*0.015+0.2*0.02=0.015+0.0045+0.004=0.0235
b)P(Texas/claim)=(0.2*0.02)/0.0235=0.1702
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