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Unformatted text preview: Probability Examples (with solutions) 1. The experiment is to roll a sixsided die. (a) Write down the sample space S , that is, list all possible outcomes of this experi ment. Solution: S = { 1 , 2 , 3 , 4 , 5 , 6 } (b) Let A be the event that die shows a number that is greater than or equal to 5. Write down the outcomes in A . Solution: A = { 5 , 6 } (c) Let B be the event that the die shows an odd number. Write down the outcomes in B Solution: B = { 1 , 3 , 5 } (d) Write down the outcome(s) in the event A B . Solution: A B = { 5 } (e) Let C be the event that the die shows a 1. Write down the outcome(s) in C . Solution: C = { 1 } (f) If all outcomes in this experiment are equallylikely, compute P ( A B ). Solution: Using the equally likely rule: P ( A B ) = num. of outcomes in A B num. of outcomes in S = 1 / 6 1 (g) If all outcomes in this experiment are equallylikely, compute P ( C B c ) Solution: Using the equally likely rule: P ( C B c ) = num. of outcomes in C B c num. of outcomes in S = num. of outcomes in num. of outcomes in S = 0 / 6 = 0 2. Suppose that for a population of 100,000 individuals: 10% of the individuals watch Hockey and Football. 35% of the individuals watch Football. 55% of the individuals watch neither Hockey nor Football. The experiment is to randomly select an individual from this population and ask about his/her football/hockey watching. Let F be the event that the randomly selected individual watches Football. Let H be the event that the randomly selected individual watches hockey. (a) Compute the probability a randomly selected individual watches either football or hockey or both, P ( F H ). Solution: In the problem statement (using the population formula), we are given that P (( F H ) c ) = 0 . 55. Using the compliment rule: P ( F H ) = 1 P (( F H ) c ) = 1 . 55 = 0 . 45 (b) Compute the probability a randomly selected individual watches hockey, P ( H ). Solution: In the problem statement (from the population formula), we are given that P ( F H ) = 0 . 10 and P ( F ) = 0 . 35, now using the union rule: P ( F H ) = P ( F ) + P ( H ) P ( F H ) solving for P ( H ) and pluggingin what we know:...
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This note was uploaded on 05/06/2011 for the course STAT 5021 taught by Professor Staff during the Spring '08 term at Minnesota.
 Spring '08
 Staff
 Probability

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