# Survey Results and Conditional Probability

#### boydoineedhelp

##### New member
Can someone please review my work and let me know if I'm doing them right? If not, please show work if I got any wrong so I know how to fix it. Thank you.

The following table shows the gender and method of payment for individuals who completed a Gas Survey. (I put dashes between the numbers and words on the chart to separate them because they get mushed to gether otherwise. There is also supposed to be a vertical line going down after debit but before total, separating the total from the rest of the data. When I try to copy it on to here it keeps messing up.)

cash - credit - debit - total

female: 9 - 14 - 8 - 31

male: 14 - 10 - 5 - 29
_________________________________________
total: 23 - 24 - 13 - 60

I am writing it this way also to help better understand the chart.
(1st horizontal line - Female: Cash 9, Credit 14, Debit 8, Total 31)
(2nd horizontal line - Male: Cash 14, Credit 10, Debit 5, Total 29)
(3rd horizontal line - Total: Cash 23, Credit 24, Debit 13, Total 60)
(1st veritcal line - Female, Male, Total)
(2nd veritacl line - Cash, 9, 14, 23)
(3rd veritcal line - Credit, 14, 10, 24)
(4th vertical line - Debit, 8, 5, 13)
(5th verital line - Total, 31, 29, 60)

Use the information in the table to answer the following questions. Leave your final answer in fraction form. Do not reduce. No decimal answers will be accepted. Write your final answer to each part on the line provided.

If one person from this study is selected at random what is the

a. Probability the person selected is a male.
29/60

b. Probability the person selected used cash.
23/60

c. Probability the person selected did not use cash. SW
24 + 13 = 37

37/60

d. Probability the person selected used cash OR debit. SW
23 + 13 = 36

36/60

e. Probability the person selected is a male OR paid cash. SW
29 + 23 = 52

52/60

f. Probability the person used cash GIVEN the person selected is a male.
14/60

g. Probability the person is a female who paid by credit.
14/60

#### soroban

##### Elite Member
Hello, boydoineedhelp!

The following table shows the gender and method of payment for individuals who completed a Gas Survey.

. . $$\displaystyle \begin{array}{c||c|c|c||c}& \text{cash} & \text{credit} & \text{debit} & \text{Total} \\ \hline\hline \text{Female} & 9 & 14 & 8 & 31 \\ \text{Male} & 14& 10 & 5 & 29 \\ \hline\hline \text{Total} & 23 & 24 & 13 & 60 \end{array}$$

Use the information in the table to answer the following questions.

If one person from this study is selected at random what is the probability that:

(a) the person selected is a male.

. . . $$\displaystyle \frac{29}{60}$$

(b) the person selected used cash.

. . . $$\displaystyle \frac{23}{60}$$

(c) the person selected did not use cash.

. . . $$\displaystyle 24 + 13 \:=\: 37 \quad\Rightarrow\quad \frac{37}{60}$$

(d) the person selected used cash or debit.

. . . $$\displaystyle 23 + 13 \:=\: 36 \quad\Rightarrow\quad \frac{36}{60}$$

Your answers to (a), (b), (c), (d) are correct . . . Good work!

(e) the person selected is a male or paid cash.

. . . $$\displaystyle 29 + 23 \:=\: 52 \quad\Rightarrow\quad \frac{52}{60}$$ . . . no
. . $$\displaystyle \begin{array}{c||c|c|c||c}& \text{cash} & \text{credit} & \text{debit} & \text{Total} \\ \hline\hline \text{Female} & 9 & & & \\ \text{Male} & 14& 10 & 5 & \\ \hline\hline \text{Total} & & & & 60 \end{array}$$

$$\displaystyle These\text{ are the people who are male or paid cash.}$$

. . . $$\displaystyle 9 + 14 + 10 + 5 \:=\:38 \quad\Rightarrow\quad \frac{38}{60}$$

(f) the person used cash given the person selected is a male.

. . . $$\displaystyle \frac{14}{60}$$ . . . no

$$\displaystyle \text{We are }given\text{ that the person is a male.}$$
$$\displaystyle \text{We are dealing with the 29 males only.}$$

$$\displaystyle \text{Of them, how many paid cash? }\:14\text{ of them.}$$

$$\displaystyle \text{Therefore: }\;P(\text{cash}\,|\text{male}) \;=\;\frac{14}{29}$$

(g) Probability the person is a female who paid by credit.

. . . $$\displaystyle \frac{14}{60}$$ . . . right!

#### boydoineedhelp

##### New member
Thanks again! I see it was the wording that got to me. I have a few more to ask about. I'll be posting them in a new topic. My homework is due tonight. I hope you can help me on a few more.