Question

Here is a biased 5-sided spinner. When the spinner is spun,it can land on red,blue,green,brown or yellow. This table gives the probabilities that the spinner will land on red or on blue or on yellow or on green.

When the spinner is spun once,the probability that the spinner lands on brown is 0.06 more than if it landed on yellow.
Jennie spins the spinner 150 times.
Work out an estimate for the number of times the spinner lands on yellow.

Answer 1

Based on the given probabilities, the estimate for the number of times the spinner lands on yellow in 150 spins is 15.

Let's denote the probability of the spinner landing on brown as "p_brown" and the probability of landing on yellow as "p_yellow." According to the information given, we have the relationship:

p_brown = p_yellow + 0.06

Now, we can set up an equation using the fact that the total sum of probabilities must equal 1:

0.15 + 0.26 + 0.33 + p_brown + p_yellow = 1

Substitute the expression for p_brown:

0.15 + 0.26 + 0.33 + (p_yellow + 0.06) + p_yellow = 1

Combine like terms:

0.74 + 2p_yellow + 0.06 = 1

Solve for p_yellow:

2p_yellow = 0.2

p_yellow = 0.1

Now, to estimate the number of times the spinner lands on yellow in 150 spins, multiply the probability by the number of spins:

Number of yellow spins = 0.1 * 150 = 15