To find how much more likely 5 acceptances are compared to 2 acceptances, we calculate the difference between their probabilities based on the histogram values.

Given probabilities from the histogram:

• $P(X = 5) = 0.17$
• $P(X = 2) = 0.16$

Difference:

$P(X = 5) - P(X = 2) = 0.17 - 0.16 = 0.01$

Interpretation:

The probability of getting 5 acceptances is 0.01 (or 1%) more likely than getting 2 acceptances.

Let me know if you want further clarification or have additional questions! Here are 5 questions related to this topic for further exploration:

1. How would the probabilities change if the selection were not random?
2. What is the probability of at least 4 acceptances out of 6 freshmen?
3. How does the histogram distribution indicate if this is a binomial distribution?
4. What is the expected number of acceptances among the 6 students?
5. How would the probabilities change if the acceptance rate increased to 70%?

Tip: For binomial probability problems, the formula $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$ is essential!