According to a report of the Nielsen Company, 70% of internet searches used the Google search engine. Assume that a sample of 21 searches is studied. Round the answers to at least four decimal places.What is the probability that exactly 17 of them used Google?

To calculate the probability that exactly 17 out of 21 searches used Google, given that 70% of internet searches use Google, we can model this as a **binomial probability** problem. 

The binomial probability formula is:

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

Where:
- \( n \) = 21 (number of trials, i.e., searches)
- \( k \) = 17 (number of successes, i.e., Google searches)
- \( p \) = 0.70 (probability of success, i.e., using Google)
- \( 1 - p = 0.30 \) (probability of failure, i.e., not using Google)
- \( \binom{n}{k} \) is the binomial coefficient, also written as \( \frac{n!}{k!(n-k)!} \)

### Step 1: Calculate the binomial coefficient

\[
\binom{21}{17} = \frac{21!}{17! \cdot (21-17)!} = \frac{21!}{17! \cdot 4!}
\]

### Step 2: Plug into the binomial probability formula

Now, I'll calculate this probability step-by-step.The probability that exactly 17 out of 21 searches used Google is approximately **0.1128** or **11.28%**, rounded to four decimal places.

Would you like further details or have any questions?

Here are five related questions you might find interesting:
1. What is the probability that fewer than 15 searches used Google?
2. What is the probability that all 21 searches used Google?
3. How would the probability change if the percentage of Google searches was 80% instead of 70%?
4. What is the expected number of Google searches in this sample?
5. How does the standard deviation of the number of Google searches compare?

**Tip:** In binomial probability problems, the expected number of successes is calculated as \( n \times p \).

According to a report of the Nielsen Company, 70% of internet searches used the Google search engine. Assume that a sample of 21 searches is studied. Round the answers to at least four decimal places. What is the probability that exactly 17 of them used Google?

Learn how to calculate the probability that exactly 17 out of 21 searches used Google, given that 70% of internet searches use Google. This binomial probability problem covers key concepts, including the binomial coefficient and the binomial probability formula. Suitable for students in Grades 10-12.

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