JohnHarrison
contestada

A spinner is divided into five equal sections numbered 1 through 5. Predict how many times out of 240 spins the spinner is most likely to stop on an odd number.
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this question is just to see how this site works

Respuesta :

mreijepatmat
There are 3 odd numbers in the set {1,2,3,4,5}

So P(ODD) = 3/5


Your question is what is the expectation of getting an odd number in 240 spins:

240 x 3/5 = 144 number of Odds

The expected number of spins out of 240 spins of the considered spinner that will likely fall on the odd number is 144

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]

For this case:

Each spin is independent of any other spin.

The spin either ends up on odd (call it success) or even number (call it failure).

Thus, modelling it with binomial distribution, we get:

  • n = number of independent bernoulli trials = 240
  • Success = bernoulli trial ending up on odd number
  • Failure = non success = bernoulli trial ending up on even number

Since there are total 5 parts in spinner from 1 to 5 as 1,2,3,4,5 and there are 3 odds, so we get:
P(Success) = p = P(Getting odd in a spin) = total odd numbers in spinner/total numbers in spinner = 3/5 (as all outcomes are supposidely equally likely).

Thus, if X = random variable tracking the total number of successes in those 240 trials, then:

[tex]X \sim B(p = 3/5 = 0.6, n = 240)[/tex]

We need expected number of times the spinner will fall on odd numbers in those 240 spins

The number of times spinner falls on odd numbers in those 240 spins is X. Thus, we get:

Expected number of times the spinner will fall on odd numbers in those 240 spins = E(X)

Since we have:[tex]X \sim B(0.6, 240)[/tex]

Thus, we get:

[tex]E(X) = np = 240 \times 0.6 = 144[/tex]

Thus, the expected number of spins out of 240 spins of the considered spinner that will likely fall on the odd number is 144

Learn more about binomial distribution here:

https://brainly.com/question/13609688

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