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just give me the correct answers for a b n c

The spinner below shows
10
equally sized slices. Karen spun the dial
20
times and got the following results.
OutcomeWhiteGreyBlackNumber of Spins
5
4
11
Fill in the table below. Round your answers to the nearest thousandth.
(a)Assuming that the spinner is fair, compute the theoretical probability of landing on black or grey.
(b)From Karen's results, compute the experimental probability of landing on black or grey.
(c)Assuming that the spinner is fair, choose the statement below that is true:
As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
The experimental and theoretical probabilities must always be equal.
As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.

1 answer

To answer the questions:

(a) Theoretical probability of landing on black or grey:

  • Since there are 10 equally sized slices, the probabilities for each color (black and grey) are as follows:
    • Probability of black = 1/10
    • Probability of grey = 1/10
  • Therefore, the theoretical probability of landing on black or grey = Probability of black + Probability of grey = 1/10 + 1/10 = 2/10 = 0.2.

Rounded to the nearest thousandth, the answer is: 0.200.

(b) Experimental probability of landing on black or grey:

  • Karen spun the spinner 20 times and got the following results:
    • Number of spins for black = 11
    • Number of spins for grey = 4
  • Therefore, the total number of spins for black or grey = 11 + 4 = 15.
  • The experimental probability of landing on black or grey = Number of spins for black or grey / Total number of spins = 15 / 20 = 0.75.

Rounded to the nearest thousandth, the answer is: 0.750.

(c) True statement regarding experimental and theoretical probabilities:

  • The correct statement is: As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

So, the final answers are: (a) 0.200
(b) 0.750
(c) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.