Question #1-(2 points) What is the probability of having a three-digit number la
ID: 3306426 • Letter: Q
Question
Question #1-(2 points) What is the probability of having a three-digit number larger than 341 among all the available three-digit numbers which are formed from the digits 0, 1,2,3,4, 5, 6, 7, 8,9, if each digit can be used only once? (a) 0.667 (b) 0.738 (c) 0.729 (d) 0.741 (e) 0.756 Question #2-(2 points) A student was interested in knowing his probability of getting an A from a course with 50 registered students. After consulting with course instructor, he was informed that 8 students got A, 23 students received B, 15 students ended up with C, and D grade was given to the rest. Based on the given information, the probability that this student received an A from this course can be estimated to be: (a) 0.137 (b) 0.143 (c) 0.160 (d) 0.163 (e) 0.168 o Please show work for all Question #3-(2 points) A pair of fair dice and two coins are tossed simultaneously. The probability of having a total of 6 from dice or having twe heads facing up is equal to: (a) 0.035 (b) 0.139 (c) 0.278 (d) 0.389 (e) 0.639Explanation / Answer
1. Total number of three digit numbers where no digit repeats (including leading 0) = 10*9*8 = 720.
If the leading digit is 0, the other two digits can come in 9*8 = 72 ways
=> Actual number of three digit numbers = 720 - 72 = 648.
Let us find the number of three digit numbers (no repeat of digits) less than or equal to 341.
If the first digit is 1, the number of three digit numbers with no repitition = 9*8 = 72.
If the first digit is 2, the number of three digit numbers with no repitition = 9*8 = 72.
If the first digit is 3, there are three choices for the second digit (0,1,2) and 8 choices for the last if the number must be less than 340. Total number of numbers = 3*8 = 24.
The other two numbers are 340 and 341.
Thus the number of numbers that are less than or equal to 341 = 72 + 72 + 24 + 2 = 170
=> Number of numbers greater than 341 = 648 - 170 = 478.
=> Probability = 478/648 = 0.738 given in option b.
2. Number of students who got A out of 50 = 8
=> Probability = 8/50 = 0.160 which is given in c.
3. The total of 6 can come only in 1 way (3 and 3) out of 36 while the two heads can come up in one way out of 4.
Probability of getting a sum of 6 on the pair of dice = 1/36.
Probability of getting both heads = 1/4.
=> Probabilility of getting a sum of 6 or both heads = 1/36 + 1/4 +1/36*1/4
= 40/144 +1/144
= 0.278 which is given in c.