We can solve this problem using the binomial probability formula since we are dealing with a fixed number of trials (25 adults), two possible outcomes (using a smartphone in meetings or not), and a constant probability (55%).

The binomial probability formula is:

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

where:

• $P(X = k)$ is the probability of exactly $k$ successes,
• $n$ is the number of trials (25 adults),
• $k$ is the number of successes (15 adults using smartphones),
• $p$ is the probability of success on a single trial (0.55),
• $1 - p$ is the probability of failure (0.45),
• $\binom{n}{k}$ is the binomial coefficient: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$.

Now let's calculate:

$P(X = 15) = \binom{25}{15} (0.55)^{15} (0.45)^{10}$

First, compute $\binom{25}{15}$:

$\binom{25}{15} = \frac{25!}{15!(25-15)!} = \frac{25!}{15!10!} = 3268760$

Now plug this into the formula:

$P(X = 15) = 3268760 \times (0.55)^{15} \times (0.45)^{10}$

Using a calculator:

$P(X = 15) \approx 3268760 \times 0.00258 \times 0.00253$ $P(X = 15) \approx 21.36\%$

Thus, the probability that exactly 15 out of 25 adults use their smartphones in meetings or classes is approximately 0.2136 or 21.36%.

Do you want further details or have any questions?

Related questions:

1. What is the probability that fewer than 10 adults use their smartphones in meetings or classes?
2. How would the probability change if only 10 adults were selected instead of 25?
3. What is the expected number of adults using smartphones in meetings from a group of 25?
4. How would you calculate the probability that more than 20 adults use their smartphones in meetings?
5. What is the variance and standard deviation for the number of adults using smartphones?

Tip: The sum of binomial probabilities over all possible outcomes equals 1, as they represent all possible results of the experiment.