Consider a multiple choice exam with 10 questions, and with 4 possible answers to each question (labeled a, b, c, and d). 1a. what is the probability of getting a perfect score just by guessing? 1b. what is the probability of getting at least one question correct, just by guessing? explain your thought process briefly. 2. each ruid is 9-digits long, but the 4th and 5th digits must both be 0. how many different ruids can there be?

(1a) 9.54e-07 (1b) 0.9437 (2)

Step-by-step explanation:

We have n = 10 questions. For each question in the multiple choice exam, we can choose the correct answer with probability p = 0.25 or an incorrect answer with probability q = 0.75 (just by guessing). Besides is reasonable to believe that questions are independent. Let X be the random variable that represents the number of correct answers (just by guessing) observed during the n = 10 questions, so, X have a binomial distribution.

(a) The probability of getting a perfect score just by guessing is

(b) The probability of getting at least one question correct, just by guessing

2. Each RUID is 9-digits long, there are 10 digits, each of the nine positions for a digit of the RUID has 10 posibilities except the 4th and 5th positions which must be both 0. For the multiplication rule there can be different RUIDS.

10010010001010010101001001010010100101010010101010010010101010110010001011010010010001

step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.