Example Situation Suppose that you are running a lottery where some number betwe
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Example Situation Suppose that you are running a lottery where some number between 1 and 40 is picked at random by a computer. Since the computer is randomly selecting the number, every number between 1 and 40, inclusive, could be selected. (This includes numbers such as , 15, and 39.999999999999999, etc.) A. What is (i.e., define) the stochastic variable in this situation? B. Describe a stochastic process that could be used in this situation. Be sure to include any assumptions that might need to make. C. Express (using Function Notation) the probability that a number selected is less than or equal to 25. D. Express (using Function Notation) the probability that a number selected is strictly greater than 36. E. What percent of the time (to four decimal places) will the numbcr sclected fall betwcen 25 and 36? Tip! Preview Tip! Preview Previcw For calculational help, use the Stat Calculator.Explanation / Answer
Rolling a single die
1) probability of rolling divisors of 6 :
Since its a single die, the possible outcomes are 1,2,3,4,5,6. All have equal probability(1/6) since its a fair die
Out of these divisors of 6 are 1,2,3,6. So P(divisors of 6) = 1/6*1/6*1/6*1/6 = 1/1296 = 0.0008
2) probability of rolling a multiple of 1: Since all(1,2,3,4,5,6) are multiples of 6 = 1/6*1/6*1/6*1/6*1/6*1/6= 1/46656 = 0.00002
3) probability of rolling an even number : There are 3 even numbers between 1-6 i.e. 2,4,6
Hence probability of rolling an even number = 1/6*1/6*1/6 = 1/216 =0.0046
4) List of all possible outcomes of rolling a single die ={1,2,3,4,5,6}
5) probability of rolling factors of 3 : Factors of 3 are 1,3
Hence probability of rolling factors of 3 = 1/6*1/6 = 1/36 = 0.0278
6) probability of rolling a 3 or smaller : 3 or smaller are 1,2,3. Hence the probability = 1/6*1/6*1/6 = 1/216 = 0.0046
7) probability of rolling a prime number: Prime numbers between 1-6 are 2,3,5 hence probability = 1/6*1/6*1/6=1/216=0.0046
8) probability of rolling factors of 4 : Factors of 4 are 1,2,4 hence the probability = 1/6*1/6*1/6 = 1/216 =0.0046
9) probability of rolling divisors of 30 : Divisors of 30 are 1,2,3,5,6 = 1/6*1/6*1/6*1/6*1/6 = 1/7776 = 0.0001
10) probability of rolling factors of 24: Factors of 24 are 1,2,3,4,6 = 1/6*1/6*1/6*1/6*1/6=1/7776=0.0001
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