Question

the expected number of heads in 500 tosses of an unbiased coin is:

Answer 1

There is a 50%, or 1/2, chance of getting heads on each flip. Each of the 500 trials is independent. Because there is a 1/2 chance of getting heads, you would expect half of them to land on heads. 500/2 = 250. You would theoretically expect  250 heads if you tossed an unbiased coin 500 times.

Answer 2

Using the binomial distribution, it is found that the expected number of heads in 500 tosses of an unbiased coin is 250.

For each coin, there are two possible outcomes, either it is heads, or it is tails. The probability of a coin being head/tails is independent of any other coin, hence the binomial distribution is used.

Binomial distribution:

Probability of x successes on n trials, with p probability.

The expected number of successes is:

$E(X) = np$

In this problem:

• 500 tosses, hence $n = 500$.
• Unbiased, that is, equally as likely to be heads or tails, hence $p = 0.5$.

The expected number of heads is:

$E(X) = np = 500(0.5) = 250$

A similar problem is given at https://brainly.com/question/24261244