To calculate the expected number of times 7 coins will fall head upward out of 100 tosses, we can use the binomial distribution formula.



The binomial distribution formula is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:
- P(X = k) is the probability of getting exactly k successes
- n is the number of independent trials
- k is the number of successes
- p is the probability of success on an individual trial
- (n choose k) is the binomial coefficient, which can be calculated as n! / (k! * (n-k)!)



In this problem, we have:
- n = 100 tosses
- k = 7 heads
- p = 0.5 (since the coin is equally likely to land heads or tails)

Plugging these values into the formula, we get:

P(X = 7) = (100 choose 7) * 0.5^7 * (1-0.5)^(100-7)
P(X = 7) = 160,075,608 * 0.0078125 * 0.4921875
P(X = 7) = 1,239,042.5 / 8

So the probability of getting exactly 7 heads out of 100 tosses is approximately 154,880.3 / 100,000, or 0.1548803.



To find the expected number of times that 7 coins will fall head upward out of 100 tosses, we multiply the probability of 7 heads by 100:

Expected number of times = 0.1548803 * 100
Expected number of times = 15.48803

So we would expect 7 coins to fall head upward approximately 15 times out of 100 tosses.



Therefore, the answer to the question "if 10 coins are tossed 100 times, how many times would you expect 7 coins to fall head upward?" is 15.

12