Respuesta :
Answer:
Close to 640 times but probably not exactly 640
Step-by-step explanation:
The expected number of times out of 800 spins that the spinner will land in the shaded region for this case is 640
How to calculate the probability of an event?
Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
How to find that a given condition can be modeled by binomial distribution?
Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]
Each of the 800 spins are independent in terms of their result from each other.
Each spin ends up either in shaded region(call it success), or non-shaded region(failure).
P(success) = P(A spin landing in shaded region) = 4/5 (as there are total 5 partition of spinner possible (assuming no other outcome possible), and that there are 4 shaded regions (favorable elementary events).
If we take X = number of successes in those 800 spins, then:
[tex]X \sim B(n = 800, p = 4/5 = 0.8)[/tex]
The expected value of X is:
[tex]E(X) = np = 800 \times 0.8 = 640[/tex]
Thus, the expected number of times out of 800 spins that the spinner will land in the shaded region for this case is 640
Learn more about binomial distribution here:
https://brainly.com/question/13609688
