Studdy AI Logo
Math  /  Data & Statistics

QuestionThe table shows the distribution, by age, of a random sample of 3910 Age Distribution of Moviegoers moviegoers ages 12-74. If one moviegoer is randomly selected from this population, find the probability, expressed as a simplified fraction, that the moviegoer is not in the 65-74 age range. \begin{tabular}{|c|c|} \hline Ages & Number \\ \hline 12−2412-24 & 1330 \\ \hline 25−4425-44 & 1080 \\ \hline 45−6445-64 & 990 \\ \hline 65−7465-74 & 510 \\ \hline \end{tabular}
The probability is □\square (Type an integer or a simplified fraction.)

Studdy Solution

STEP 1

What is this asking? Out of a group of moviegoers, what are the chances of picking someone *not* between 65 and 74 years old? Watch out! Don't forget, we want the probability of *not* picking someone in that age range!

STEP 2

1. Find the total number of moviegoers.
2. Find the number of moviegoers *not* in the target age range.
3. Calculate the probability.

STEP 3

We're given the number of moviegoers in each age group.
To find the **total**, we need to add them all up!
This gives us the **total population** we're considering.

STEP 4

Total Moviegoers=1330+1080+990+510=3910 \text{Total Moviegoers} = 1330 + 1080 + 990 + 510 = \mathbf{3910} So, there are a whopping **3910** moviegoers in total!

STEP 5

We know the total number of moviegoers, and we know how many are between 65 and 74.
To find the number *outside* that age range, we subtract!
This is like removing the 65-74 group from the total.

STEP 6

Moviegoers Not in 65-74=Total Moviegoers−Moviegoers in 65-74 \text{Moviegoers Not in 65-74} = \text{Total Moviegoers} - \text{Moviegoers in 65-74} Moviegoers Not in 65-74=3910−510=3400 \text{Moviegoers Not in 65-74} = 3910 - 510 = \mathbf{3400} So, there are **3400** moviegoers *not* in the 65-74 age range.

STEP 7

Probability is all about comparing what we *want* to the *total possibilities*.
We want to pick someone *not* in the 65-74 range, and there are 3400 such people.
The total number of moviegoers is 3910.
Let's divide!

STEP 8

Probability=Number of moviegoers not in 65-74Total number of moviegoers \text{Probability} = \frac{\text{Number of moviegoers not in 65-74}}{\text{Total number of moviegoers}} Probability=34003910 \text{Probability} = \frac{3400}{3910}

STEP 9

Now, let's simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 10.
This gives us: 34003910=3400÷103910÷10=340391 \frac{3400}{3910} = \frac{3400 \div 10}{3910 \div 10} = \frac{340}{391} We're dividing both by 10 to make the fraction simpler, and because it's the biggest number that goes into both evenly.
So, the probability is 340391\frac{\mathbf{340}}{\mathbf{391}}!

STEP 10

The probability that a randomly selected moviegoer is not in the 65-74 age range is 340391\frac{340}{391}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord