Respuesta :
Answer:
(5/3) (0.60)^3(0.40)^2
Step-by-step explanation:
Using the binomial distribution, it is found that there is a 0.3456 = 34.56% probability that she gets exactly 3 heads.
For each coin flipped, there are only two possible outcomes, either it is heads, or it is tails. The result of a coin flip is independent of any other coin flip, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- The coin is flipped 5 times, hence [tex]n = 5[/tex].
- 60% of the time, it comes up heads, hence [tex]p = 0.6[/tex].
The probability is P(X = 3), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.6)^{3}.(0.4)^{2} = 0.3456[/tex]
0.3456 = 34.56% probability that she gets exactly 3 heads.
A similar problem is given at https://brainly.com/question/21270423
