A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. If you spin this

Question

A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.
If you spin this spinner 1000 times, how many times do you expect it to land on Red?
(Hint: Find n first)

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Phúc Điền 4 years 2021-07-24T04:02:46+00:00 1 Answers 6 views 0

Answers ( )

  1. thanhcong
    0
    2021-07-24T04:04:38+00:00
    Reply

    Given:

    A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.

    To find:

    The expected number of times it land on Red if you spin this spinner 1000 times.

    Solution:

    A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. So,

    n+3n+8n=240

    12n=240

    n=\dfrac{240}{12}

    n=20

    The value of n is 20. It means the spinner land on red 20 times if the spinner was spun 240 times. So, the probability of getting red is:

    P(Red)=\dfrac{20}{240}

    P(Red)=\dfrac{1}{12}

    If you spin this spinner 1000 times, then the expected number of times to getting red is:

    E(Red)=1000\times P(Red)

    E(Red)=1000\times \dfrac{1}{12}

    E(Red)=83.333...

    E(Red)\approx 83

    Therefore, the expected number of times to land on red is 83.

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