# Help with this probability problem?

#### ElleWoods69

##### New member
Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers carry a credit card balance?
0.0375
0.1390
0.1015
0.3133

Thank you!!

#### MarkFL

##### Super Moderator
Staff member
Hello, and welcome to FMH!

Suppose we pick just one person at random. What is the probability that that one person carries a credit card balance?

#### ElleWoods69

##### New member
Hello, and welcome to FMH!

Suppose we pick just one person at random. What is the probability that that one person carries a credit card balance?
1 in 44? So .0227??

#### MarkFL

##### Super Moderator
Staff member
1 in 44? So .0227??
No, we are told 44% of people carry a balance, so the probability when picking 1 person at random that they will carry a balance is:

$$\displaystyle 44\%=\frac{44}{100}=0.44$$

Now, suppose we pick 2 people at random, what is the probability that the first person will carry a balance AND the second person will carry a balance?

#### tkhunny

##### Moderator
Staff member
What is the probability that all consumers carry a credit card balance?
0

#### Jomo

##### Elite Member
You can't argue with that logic.

#### Otis

##### Senior Member
Good catch, tkhunny. Replace the phrase "all consumers" with "all four of them".

#### Jomo

##### Elite Member
On an exam if the question was posed that way (and I caught it) I would put down 0 and just smile because I got free points. So I though! There would always be someone who would point out an error like that to our instructor.

#### pka

##### Elite Member
Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers carry a credit card balance?
Group of answer choices: 0.0375, 0.1390, 0.1015, 0.3133
Note the wording it says that of the people who do have credit cards, 44% of those carry a balance.
That does not mean that 44% have credit cards. In fact we need to know what percent have credit cards.
Based upon the replies so far, we need more careful readings.

#### Jomo

##### Elite Member
Note the wording it says that of the people who do have credit cards, 44% of those carry a balance.
That does not mean that 44% have credit cards. In fact we need to know what percent have credit cards.
Based upon the replies so far, we need more careful readings.
???

#### pka

##### Elite Member
Three question marks? It is a simple English sentence: Forty-four percent of consumers with credit cards carry balances.
It means that of all who have credit cards, 44% or those carry a balance month to month.
It does not mean that 44% of all customers have credit cards. That is the percent we need to work the problem.
I suspect that a non-native English speaker wrote this question wrote this question.

#### Jomo

##### Elite Member
Three question marks? It is a simple English sentence: Forty-four percent of consumers with credit cards carry balances.
It means that of all who have credit cards, 44% or those carry a balance month to month.
It does not mean that 44% of all customers have credit cards. That is the percent we need to work the problem.
I suspect that a non-native English speaker wrote this question wrote this question.
I understand what the 44% means. To solve the problem I do not see why you need to know what percent of customer have a credit card.

If 44% of customers with credit cards have a monthly balance than there must be at least one person who does not carry a monthly balance. Sure that one person I speak of has a credit card but who cares since the problem asks what is the probability that all consumers carry a credit card balance? The answer is clearly 0.

#### Otis

##### Senior Member
… the problem asks what is the probability that all consumers carry a credit card balance?
Jomo, you don't think it's a misprint?

$$\;$$

#### MarkFL

##### Super Moderator
Staff member
I suspect the problem should read something like:

Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers selected carry a credit card balance?

pka

#### Jomo

##### Elite Member
Jomo, you don't think it's a misprint?

$$\;$$
Yes I do, but either way pka post is not correct.