To answer this question, we need to use the experimental data to estimate the probability of getting two heads in one try. Then, we can use the binomial distribution formula to calculate the probability of getting two heads in 100 tries.
The experimental data shows that out of 50 trials, Cassandra got two heads 14 times. Therefore, the estimated probability of getting two heads in one try is
14/50=0.28
The binomial distribution formula gives the probability of getting exactly x successes in n independent trials, where each trial has a probability of success p The formula is:
P(X=x) = (n/x) p^x(1-p)^n-x
where n/x is the binomial coefficient, which can be calculated as:
N/x=n!/x!(n-x)!
where n! is the factorial of n, which is the product of all positive integers less than or equal to n.
In this case, we want to find the probability of getting exactly two heads (x=2) in 100 trials (n=100), where each trial has a probability of 0.28 (p=0.28) of getting two heads. Plugging these values into the formula, we get:
P(X=2) = {100}/{2}(0.28)^2(1-0.28)^{100-2}
P(X=2) = \frac{100!}{2!(100-2)!}(0.28)^2(0.72)^{98}
$$P(X=2) =4.05047459×10−12
This is a very small number, which means that it is very unlikely that Cassandra will flip two heads in 100 tries, based on the experimental data. Therefore, the answer is:
4.05047459×10−12