Math115a Probability Worksheet – Due Monday, February 2 Be sure to use correct mathematical notation and define your events when applicable.1. Suppose two dice are rolled and the sum is noted. Below is the sample space for this experiment. 1,1 2,1 3,1 4,1 5,1 6,11, 2 2,2 3, 2 4,2 5, 2 6, 21,3 2,3 3,3 4,3 5,3 6,31, 4 2,4 3, 4 4,4 5, 4 6, 41,5 2,5 3,5 4,5 5,5 6,51,6 2,6 3, 6 4,6 5,6 6,6S Let Ethe event that a sum of 6 is rolledLet Fthe event that the sum is an odd numbera. Find )(EPb. Find )( FEP c. Find )(CEP2. The probability that you get a raise is 0.68, the probability that you get your own office is 0.41, and the probability that you get a raise and your own office is 0.24. a. Find the probability that you get a raise or your own office. b. Find the probability that you do not get a raise.c. Find the probability that you get a raise but not your own office.3. Best Builders has bid on contracts for the construction of two large office buildings. The owner of the company estimates that the probability of being awarded the first contract is 0.4, the probability of beingawarded the second contract is 0.6, and the probability of being awarded the first or the second contract is 0.9. a. What is the owner’s estimate of the probability of being awarded both of the contracts?b. What is the owner’s estimate of the probability of being awarded neither of the contracts?4. A fair coin is flipped 4 times.a. Write out the sample space for this experiment.b. What is the probability of obtaining exactly one tail?c. What is the probability of obtaining a head on the first flip and a tail on the third flip?d. What is the probability of obtaining 0
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