Question

We toss 3 coins 100,000 times. How many times do we expect to see "Exactly 1 head" appearing? Responses 50,000 50,000 37,500 37,500 12,500 12,500 3,750

Answer 1

The correct answer is B.

To determine the expected number of times "Exactly 1 Head" appears when tossing 3 coins 100,000 times, we can use the binomial probability formula. The probability of getting exactly 1 head in a single coin toss is
`\( \binom{3}{1} * \left((1)/(2)\right)^1 * \left((1)/(2)\right)^2 \)`, where
`\( \binom{3}{1} \)` is the number of ways to choose 1 head from 3 coins.

The expected number of occurrences (μ) can be calculated by multiplying the probability of success by the number of trials:
`\( μ = n * p \),` where
`\( n \)` is the number of trials (100,000) and
`\( p \)` is the probability of success.

For this case,
`\( p = \binom{3}{1} * \left((1)/(2)\right)^1 * \left((1)/(2)\right)^2 \). Therefore, \( μ = 100,000 * p \).`

`\[ μ = 100,000 * \binom{3}{1} * \left((1)/(2)\right)^1 * \left((1)/(2)\right)^2 \]`

`\[ μ = 100,000 * 3 * (1)/(2) * (1)/(4) \]`

`\[ μ = 37,500 \]`

Therefore, the expected number of times "Exactly 1 Head" appears when tossing 3 coins 100,000 times is 37,500.

Question:

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

A. 12,500

B. 37,500

C. 3,750

D. 50,000