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The image contains a probability problem involving a scenario where Cade is filling out summer job applications. Here's a detailed breakdown:

### Problem:
1. Cade is submitting **5** applications.
2. The probability that each of his applications gets a job offer is **61%** (or 0.61).
3. You are asked to calculate the probability that **3 out of the 5 applications** result in job offers.
4. The result should be given as a decimal rounded to four decimal places.

### Solution Approach:

This is a **binomial probability** problem where:
- \( n = 5 \) (the number of trials, i.e., applications submitted)
- \( k = 3 \) (the number of successes, i.e., job offers)
- \( p = 0.61 \) (the probability of success for each trial, i.e., getting a job offer)
- \( q = 1 - p = 0.39 \) (the probability of failure for each trial, i.e., not getting a job offer)

The binomial probability formula is:

\[
P(k) = \binom{n}{k} p^k (1 - p)^{n-k}
\]

Where:
- \( \binom{n}{k} \) is the binomial coefficient calculated as:

\[
\binom{n}{k} = \frac{n!}{k!(n-k)!}
\]

I will now compute this probability.The probability that Cade will receive job offers for exactly 3 out of the 5 applications is **0.3452**, rounded to four decimal places.

Would you like any more details or have any further questions?

Here are 5 related questions you might explore:
1. How do you calculate the probability of receiving offers for exactly 4 out of 5 applications?
2. What is the probability that Cade receives at least one job offer from his 5 applications?
3. How does the probability change if the chance of getting a job offer increases to 70%?
4. What if Cade submits 7 applications instead of 5? How does this affect the probability for 3 offers?
5. How do you calculate the expected number of job offers Cade will receive?

**Tip:** In binomial probability problems, it's useful to identify whether you need the probability for "exactly," "at least," or "at most" a certain number of successes. These nuances affect the approach!

Cade is filling out summer job applications, so that he can earn money to buy a car. Of the 5 job he's applying for, 3 are babysitting jobs. If Cade randomly picks 5 applications to submit today, what is the probability that exactly 3 of the chosen applications are for babysitting jobs?

Explore how to solve a binomial probability problem involving Cade's job applications. Learn to calculate the probability of exactly 3 out of 5 applications receiving job offers with detailed step-by-step instructions. This problem covers key probability concepts, including binomial distribution and the binomial coefficient formula, suitable for students in Grades 9-12.

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