Questions: A spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 11?

Solution Steps

To find the probability that the spinner will land on a number that is not a multiple of 11, we need to:

1. Determine the total number of possible outcomes (which is 50, since the spinner has numbers 1 through 50).
2. Identify the numbers that are multiples of 11 within this range.
3. Subtract the count of multiples of 11 from the total number of outcomes to get the count of numbers that are not multiples of 11.
4. Calculate the probability by dividing the count of numbers that are not multiples of 11 by the total number of outcomes.

The spinner contains numbers from 1 to 50, so the total number of possible outcomes is: \[ \text{Total outcomes} = 50 \]

We need to find the numbers between 1 and 50 that are multiples of 11. These numbers are: \[ 11, 22, 33, 44 \] Thus, the count of multiples of 11 is: \[ \text{Count of multiples of 11} = 4 \]

Subtract the count of multiples of 11 from the total number of outcomes: \[ \text{Count of numbers not multiples of 11} = 50 - 4 = 46 \]

The probability that the spinner will land on a number that is not a multiple of 11 is given by: \[ P(\text{not a multiple of 11}) = \frac{\text{Count of numbers not multiples of 11}}{\text{Total outcomes}} = \frac{46}{50} = 0.92 \]

Final Answer