The spinner is divided into 12 equal parts if you spin the spinner 100 times how many times do you expect the spinner to stop on a number less than 10?

Answer 1

∙It will be spun on a number less than 10 in 75 times if you spin it 100 times.

Explanation:

Let x be the random variable, x = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

The probability for any outcome is P(x) = 1/12. It is a flat probability distribution.

The probability that when you spin the spinner the outcome is a number greater than

10 is:

P(10 ≤ x ≤ 12) = P(x = 10) + P(x = 11) + P(x = 12 ) = 3/12 = 1/4

The probability of the complement event (that the outcome is a number smaller than 10) is: P(x < 10) = 1 - 1/4 = 3/4.

So the expected number of times the spinner outcome will be a number smaller than 10 is:

P(No. outcomes x<10 in 100 spins) = 100 ∙ P(x<10) = 100 ∙ 3/4 = 75