Question

We toss 3 coins 100,000 times. How many times do we expect to see "Exactly 1 head" appearing?
Answer

12,500

37,500

3,750

50,000

Answer 1

Assuming that the coins are fair, the probability of one coin being a head is 1/2 and the probability of one coin being a tail is also 1/2. When tossing three coins, the probability of one being a head is given by:
\[\large \frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}\]
However there are three possible ways in which one of the three coins can be a head, therefore the probability of one coin being a head when three fair coins are tossed is 3/8.
Now you can find the expected number of times that exactly one head will appear in 100,000 tosses by multiplying 100,000 by 3/8.