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A spinner has three equally sized regions: blue, red, and green. Jonny spins the spinner 3 times and gets 3 blues in a row. If he spins the spinner 297 more times, how many more blues is he most likely to get

Respuesta :

Using the binomial distribution, it is found that he is most likely to get 99 blues.

For each spin, there are only two possible outcomes, either it lands on blue, or it does not. The probability of a spin landing on blue is independent of any other spin, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability of a success on each trial.  

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this problem:

  • One-third of the regions are blue, hence [tex]p = \frac{1}{3}[/tex].
  • 297 more spins, hence [tex]n = 297[/tex].

Thus, the expected value is:

[tex]E(X) = np = 297\frac{1}{3} = 99[/tex]

He is most likely to get 99 blues.

A similar problem is given at https://brainly.com/question/24261244

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