Assignment 2: MAT 1100 Quantitative Reasoning Module 4 Lesson 1

This assignment solution covers various probability problems from the MAT 1100 Quantitative Reasoning course. The problems include determining mutually exclusive events, calculating probabilities for dice rolls and spinners, and finding probabilities based on given distributions. Specific questions involve finding the probability of the sum of two dice being 5 or 11, the probability of a spinner landing on an odd number or a multiple of 9, and finding probabilities based on age distributions and family sizes. Additional problems involve calculating the probability of drawing a card that is not an ace, the probability of failing a statistics test, and probabilities related to marble selection and degree distributions. The solution provides step-by-step answers and explanations for each problem, demonstrating key concepts in probability and statistics.

MAT 1100 Quantitative Reasoning Module 4 Lesson 1 Assignment 2
Name___________________________________
Decide whether or not the events are mutually exclusive.
1) Events A and B defined as follows A card is drawn at random from a deck of cards. Event A is that
the card obtained is a queen card and B is the event that the card obtained is a three.
A) Yes B) No
Answer: Yes
2) Play tennis and play chess.
A) Yes B) No
Answer; No
Find the probability.
3) When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that
the sum of the numbers on the dice is 5 or 11?
Sum 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Prob (Sum is 5 or 11)¿ 4+ 2
36 =1
6
4) A spinner has regions numbered 1 through 15. What is the probability that the spinner will stop on
an odd number or a multiple of 9?
Prob (odd no. or a multiple of 9) ¿ 8
15
Find the indicated probability.
5) The age distribution of students at a community college is given below.
Age (years)Number of students (f)
1112
A student from the community college is selected at random. Find the probability that the student is
less than or equal 25. Round approximations to three decimal places.
Prob (less than 25)¿ 1− prob ( greater than25 )

MAT 1100 Quantitative Reasoning Module 4 Lesson 1 Assignment 2
¿ 1− 209+59+26
1112 =0.736
6) The table shows the distribution of family size in a certain U.S. city
Family Size Probability
2 0.432
3 0.245
4 0.199
5 0.081
6 0.028
7+ 0.015
A family is selected at random from the city. Find the probability that the size of the family is less than
4. Round approximations to three decimal places.
Prob (less than 4)¿ prob ( 2 ) + prob (3 )=0.432+0.245=0.677
7) A card is drawn at random from a standard 52-card deck. Find the probability that the card is not
an ace.
Prob (not an ace) ¿ 1− 4
52 =0.9231
8) The probability that Luis will pass his statistics test is 0.69. Find the probability that he will fail his
statistics test.
prob ( fail )=1−0.69=0.31
9) A bag contains 7 red marbles, 2 blue marbles, and 1 green marble. If a marble is selected at
random, what is the probability that it is not green?
Prob (not green)¿ 1− 1
10 =0.9
10) The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major Frequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Business 1676
Engineering 868
9313
What is the probability that a randomly selected degree is not in Physics?
Prob (not physics)¿ 1− 856
9313 =0.9081