Question

the spinner below shows 10 equally sized slices. Mal spun the dial 500 timesround to the nearest thousandth A: compute the experimental probability of landing on Grey or blackB: assuming that the spinner is fair compute the theoretical probability of landing on grey or blackC: see picture

Answer 1

ANSWERS

A) P(grey or black) = 0.626 (experimental)

B) P(grey or black) = 0.6 (theoretical)

C) The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.

Step-by-step explanation

A) The experimental probability is the quotient between the number of times the event occurred and the number of repetitions of the experiment. In this case, Mai spun the dial 500 times - this is the repetitions of the experiment, and got grey 172 times and black 141 times. Thus, the experimental probability of landing on grey or black is,

`P(grey.or.black)=(172+141)/(500)=(313)/(500)=0.626`

B) The theoretical probability, on the other hand, is based on how many slices are in the spinner and the colors of each. In this case, the spinner has 10 slices, of which 3 are black, 3 are grey and 4 are white. Also, we have to assume that the spinner is fair - i.e. it is equally likely to land on each slice. Thus, the theoretical probability is,

`P(grey.or.black)=(3+3)/(10)=(6)/(10)=(3)/(5)=0.6`

C) As we can see in the experimental and theoretical probabilities found in parts A and B, the results are pretty close with just a few decimals of difference.

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