Question

A spinner has three sections which are coloured blue, yellow and pink. harley spun the spinner 100 times in total. the frequency of spins that landed on yellow was 45. the ratio of the frequency of blue to the frequency of yellow was 4: 9. what is the estimated probability of the spinner landing on pink? give your answer as a decimal.

Answer 1

The estimated probability of the spinner landing on pink is 0.35. This is found by first determining the frequency of spins for blue based on the given ratio to yellow, then subtracting the sum of blue and yellow spins from the total spins.

Step-by-step explanation:

To estimate the probability of the spinner landing on pink, we first need to find the frequencies of spins for blue and pink, given the frequency for yellow and the ratio of the frequencies of blue to yellow. The frequency for yellow is 45, and the ratio of blue to yellow is 4:9. Since the ratio is equivalent to frequency, we can set up a proportion where 4 is to 9 as the frequency of blue (let's call it fblue) is to 45:

4/9 = fblue/45

By solving this equation, we find that fblue is equal to 20. As there were 100 spins in total and we have 45 yellow and 20 blue, we can find the frequency for pink (fpink) by subtracting the sum of blue and yellow from the total:

100 - 45 - 20 = fpink

fpink is, therefore, 35. To find the estimated probability of landing on pink, we divide fpink by the total number of spins:

P(pink) = 35 / 100 = 0.35

Therefore, the estimated probability of the spinner landing on pink is 0.35, or 35%.