Week 2 Discussion Due Wednesday You have a biased dice (with six faces numbered 1,2,3,4,5 and 6) in that even numbers are twice as likely as odd numbers to show. You toss the dice 15 times. What is the probability that 1-An even number would show up 5 times? 2-1 would show up five times? 1-Can it be formulated as a Binomial distribution for answering (a)? If so, how would you solve it? 2-Can it be formulated as a Binomial distribution for answering (b)? If so, how would you solve it? Assignment 2.1: Calculating Probability Due Date: Day 7 Sunday Value: 12.5 points Please provide solutions to the following problems. Please use Excel to solve the problems and submit the Excel spreadsheet. Ans: On a normal die the probability of rolling an even number is P(E) = 0.5 and the probability of rolling an odd is P(O) = 0.5. Rolling an odd or an even number are mutual exclusive outcomes meaning their probabilities of success will always sum to 1. Thus giving us the formula P(E) + P(O) = 1. If P(E) = P(O) * 2, we can use substitution to form the equation P(O) + P(O) * 2 = 1 and solve for P(O) on the weighted die. On the weighted die P(O) = 1/3 and the P(E) = 2/3. The same steps are followed from above to solve for the probability of rolling a one, P(1). Knowing that P(O) = (1/3) we just divide (1/3) by 3 and come up with P(1) = 1/9. Rolling an even number 4 times or rolling the number 1 five times meets the criteria for binomial distribution (a. there must be set number or trials, b. there are only two mutually exclusive outcomes success or failure with the probability of both summing to 1. c. The probability of each outcome doesn't change from one trial to the next). So, binomial distribution will be used to solve for both questions. Calculations: Binomial Probability: P(x) = nCr * P(success)^r * P(failure)^(n-r) 1. 5C15 * (2/3)^5 * (1/3)^10 = 6.6 * 10^-3 or 0.007 2. 5C15 * (1/9)^5 * (8/9)^10 = 1.56 * 10^-2 or 0.016 Answer: 1. 0.007 2. 0. 016 Erick Assignment 2.1 Directions Here we would use the Binomial Distribution. If you start typing '=Binomdist' . A fair coin is tossed 15 times, calculate the probability of getting 0 heads or 15 heads A biased coin with probability of head being .6 is tossed 12 times. What is the probability that number of head would be more than 4 but less than or equal to 10. You have a biased dice (with six faces numbered 1,2,3,4,5 and 6) in that odd numbers are thrice as likely as even numbers to show. You toss the dice 10 times. What is the probability that an even number would show up 5 times. If z has a standard normal distribution, calculate the following probability. P(-.3z10) If x has a normal distribution with mean 15 and standard deviation 2, calculate the following probabilities: P(1x<15)