From experience, the manager of Kramer's Book Mart knows that 50% of the people who are browsing in the store will make a purchase. What is the probability that among ten people who are browsing in the store, at least two will make a purchase? (Round your answer to four decimal places.)

the probability that n person buy the book is (0.5)^n

so the probability that at least two people buy a book is (0.5)^2 + (0.5)^3 ....... (0.5)^10
which is equal to 0.498046875

Again here the keyword is "among" 10 people.

Check that the conditions of binomial distribution are satisfied (ref. the airplane problem).

Then proceed with the calculation of "at least two" out of 10, namely "not zero", "not one" out of 10.

Instead of calculating B(2,10,0.5)+B(3,10,0.5)+...+B(10,10,0.5), we calculate the complement, i.e.
P(x>=2)
=1-P(x<)
=1-(P(x=0)+P(x=1))
=1-(B(0,10,0.5)+B(1,10,0.5))

See the airplane problem for the formula for B(x,n,p):
https://www.jiskha.com/display.cgi?id=1499053975

To calculate the probability that at least two out of ten people will make a purchase, we can use the binomial probability formula.

The binomial probability formula is:

P(x) = C(n, x) * p^x * (1-p)^(n-x)

Where:
P(x) is the probability of x successes occurring,
C(n, x) is the number of combinations of n items taken x at a time,
p is the probability of a single success occurring,
and (1-p) is the probability of a single failure occurring.

In this case, we want to find the probability that at least two out of ten people will make a purchase, given that the probability of a single person making a purchase is 0.50 (50%).

To find the probability, we need to calculate the individual probabilities for each possible combination of people making a purchase (2, 3, 4, ..., 10) and then sum them up.

P(at least 2 purchases) = P(2 purchases) + P(3 purchases) + P(4 purchases) + ... + P(10 purchases)

Substituting the values into the binomial probability formula:

P(at least 2 purchases) = [C(10, 2) * 0.50^2 * (1-0.50)^(10-2)] + [C(10, 3) * 0.50^3 * (1-0.50)^(10-3)] + [C(10, 4) * 0.50^4 * (1-0.50)^(10-4)] + ... + [C(10, 10) * 0.50^10 * (1-0.50)^(10-10)]

Now we can use a calculator, spreadsheet software, or statistical software to calculate each individual probability and sum them up. Rounding the final result to four decimal places will give us the answer.