Answer:
The probability is 0.33696
Step-by-step explanation:
The probability that the outcome will be heads x times is calculated using the following equation:
[tex]P(x) = nCx*p^{x} *(1-p)^{n-x}[/tex]
nCx is calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
This apply for variables that follows a binomial distribution. In which we have n independent and identical events with two possibles results: success and fail with a probability p and 1-p respectively.
So, In this case, n is equal to 5, and p is equal to 0.6 because we are going to call success the event in which the outcome of the coin is head.
Then, the probability that the outcome will be heads at least 4 times is calculated as:
P = P(4) + P(5)
Where P(4) is:
[tex]P(4) = 5C4*0.6^{4} *(1-0.6)^{5-4}[/tex]
P(4)=0.2592
And P(5) is:
[tex]P(5) = 5C5*0.6^{5} *(1-0.6)^{5-5}[/tex]
P(4)=0.07776
Finally, the probability is:
P = 0.2592 + 0.07776
P = 0.33696
