# Finding Probability of Real-life Situations

Find the indicated probability.

1) Two fair dice are rolled. What is the probability that a sum of 6 or 11 is obtained? 1) _______

A) 7/6 B) 17/36 C) 1/66 D) 7/36

Find the simple interest. Assume a 360-day year. Round results to the nearest cent.

2) $ 49,417 at 7.7% for 17 months 2) _______

A) $ 5390.57 B) $ 5435.87 C) $ 5073.48 D) $ 5707.66

A die is rolled twice. Write the indicated event in set notation.

4) Both rolls are even. 4) _______

A) {(2, 2), (2, 4), (2, 6)}

B) {(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}

C) {(2, 2), (4, 4), (6, 6)}

D) {(2, 4), (2, 6), (4, 2), (4, 6), (6, 2), (6, 4)}

Find the indicated probability.

5) A single card is drawn from a standard 52-card deck. Find the probability the card is a heart given that it is red. 5) _______

A) ½ B) 1 C) ¾ D) 0

Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated.

6) $ 2600 at 6% compounded annually for 10 yr. 6) _______

A) $ 1538.94 B) $ 1451.83 C) $ 1148.17 D) $ 4656.20

Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end of each year for 20 years at the given interest rate, compounded annually.

7) $ 750 at 3% 7) _______

A) $ 11,158.12 B) $ 11,150.62 C) $ 10,742.40 D) $ 11,561.25

Write the sample space for the given experiment.

9) A day of the week is selected at random 9) _______

A) 7

B) {1, 2, 3, 4, 5, 6, 7}

C){weekend, weekday}

D) {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Find the simple interest. Assume a 360-day year. Round results to the nearest cent.

10) $ 4414 at 10% for 5 months 10) ______

A) $ 220.70 B) $ 185.46 C) $ 147.13 D) $ 183.92

Find the compound amount for the deposit. Round to the nearest cent.

11) $ 2000 at 4% compounded annually for 20 years 11) ______

A) $ 3600.00 B) $ 4213.70 C) $ 3520.00 D) $ 4382.25

Determine whether the given events are mutually exclusive.

12) Knowing Spanish and knowing Chinese 12) ______

A) Yes B) No

Find the payment necessary to amortize the loan.

13) $ 1500; 6% compounded annually; 7 annual payments 13) ______

A) $ 271.33 B) $ 241.55 C) $ 305.05 D) $ 268.70

Shade the Venn diagram to represent the set.

14) A' ∪ (A ∩ B)

14) ______

A)

B)

C)

Find the indicated term of the geometric sequence.

15) a = 4, r = 2; Find the 15th term. 15) ______

A) 262,144 B) 65,536 C) 32,768 D) 16,384

A die is rolled twice. Write the indicated event in set notation.

16) The first roll is a 1. 16) ______

A) {( 1, 1), ( 1, 2), ( 1, 3), ( 1, 4), ( 1, 5), ( 1, 6)}

B) {( 1, 3)}

C) {( 1, 1), ( 1, 2), ( 1, 4), ( 1, 5), ( 1, 6)}

D) {( 1, 1), ( 1, 3), ( 1, 5)}

Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points.

17) 9% compounded semiannually 17) ______

A) 9.38% B) 9.00% C) 9.31% D) 9.20%

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

Tell whether the statement is true or false.

18) 11 ∈ { 22, 33, 44, 55, 66} 18) ______

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use a Venn diagram to answer the question.

19) At East Zone University (EZU) there are 391 students taking College Algebra or Calculus. 194 are taking College Algebra, 249 are taking Calculus, and 52 are taking both College Algebra and Calculus. How many are taking Calculus but not Algebra? 1 19) ______

A) 339 B) 90 C) 197 D) 142

Find the indicated probability.

20) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.

20) ______

A) 1/6 B) ½ C) 1 D) 0

Find the present value of the ordinary annuity.

21) Payments of $ 450 made annually for 13 years at 6% compounded annually 21) ______

A) $ 4182.75 B) $ 3772.71 C) $ 3982.28 D) $ 3983.71

Determine whether the given events are mutually exclusive.

22) Being a male and being a nurse 22) ______

A) No B) Yes

https://brainmass.com/math/calculus-and-analysis/finding-probability-real-life-situations-247595

#### Solution Summary

Step by step solutions to all the problems are provided.

Find mean and standard deviation from probability distribution

Dogs Households

0 1327

1 402

2 162

3 47

4 28

5 11

(a)

Use a frequency distribution to construct a probability distribution

x P(x)

0

1

2

3

4

5

Round to the nearest Thousandth as needed

Dogs 0 1 2 3 4 5

Households 1327 402 162 47 28 11

(b) Find the mean of the probability distribution

U = (Round to nearest tenth as needed)

c. Find the variance of the probability distribution.

Variance = (Round to nearest tenth as needed)

d. Find the standard deviation of probability distribution.

Standard deviation = (Round to nearest tenth as needed)

e. Interpret the results of the context of the real-life situation

(Choose One)

(a) A household on average has 0.8 dog with a standard deviation of 0.9 dog

(b) A household on average has 0.5 dog with a standard deviation of 0.9 dog

(c) A household on average has 0.5 dog with a standard deviation of 11 dog

(d) A household on average has 0.9 dog with a standard deviation of 0.5 dog