Question

If we toss a fair coin 50 times what is the likelihood that we land on heads 30 times or more in percentage?

Answer 1

Answer 2

The probability of getting heads on any given flip of a fair coin is 0.5 (assuming the coin is unbiased). If we flip a coin 50 times, the number of heads we get follows a binomial distribution with n = 50 and p = 0.5.

To find the probability of getting 30 or more heads, we can use the cumulative distribution function (CDF) of the binomial distribution. Many statistical software packages and calculators have built-in functions for this, but we can also use the normal approximation to the binomial distribution for an approximate answer.

Using the normal approximation, we can approximate the binomial distribution with a normal distribution with mean μ = np = 50 * 0.5 = 25 and standard deviation σ = sqrt(np(1-p)) = sqrt(50 * 0.5 * 0.5) = 3.54.

We can then standardize the distribution and calculate the area under the curve to the right of x = 29.5 (since we want the probability of getting 30 or more heads).

z = (x - μ) / σ = (29.5 - 25) / 3.54 = 1.35

Using a standard normal distribution table or calculator, we can find that the area under the curve to the right of z = 1.35 is 0.0885.

Therefore, the likelihood of getting 30 or more heads in 50 coin flips is approximately 8.85%, or 0.0885 in decimal form.