The probability of getting a head on the first toss is 0.5, regardless of the results of the other tosses.
Given that there were 4 heads in the 10 tosses, we can use Bayes' Theorem to find the probability that the first toss was a head:
P(First toss was head | 4 heads in 10 tosses) = P(4 heads in 10 tosses | First toss was head) * P(First toss was head) / P(4 heads in 10 tosses)
We know that P(First toss was head) = 0.5, and we can calculate P(4 heads in 10 tosses | First toss was head) using the binomial distribution:
P(4 heads in 10 tosses | First toss was head) = (10 choose 4) * (0.5)^4 * (0.5)^6 = 210 * 0.0625 * 0.015625 = 0.206
To calculate P(4 heads in 10 tosses), we can use the binomial distribution again:
P(4 heads in 10 tosses) = (10 choose 4) * (0.5)^4 * (0.5)^6 = 210 * 0.0625 * 0.015625 + 210 * 0.9375 * 0.984375 = 0.2051
Therefore, we can calculate the probability that the first toss was a head given that there were 4 heads in 10 tosses:
P(First toss was head | 4 heads in 10 tosses) = 0.206 * 0.5 / 0.2051 = 0.503
So the probability that the first toss was a head given that there were 4 heads in 10 tosses is approximately 0.503.