Probability: Question 1

Worked solution

Part (a): Probability of yellow

For a single spin, the spinner must land on exactly one of the four colours, so the probabilities of all the possible outcomes add up to 1:

$P(\text{red}) + P(\text{blue}) + P(\text{green}) + P(\text{yellow}) = 1$

Substitute the known values:

$0.15 + 0.4 + 0.25 + P(\text{yellow}) = 1$

Add the three given probabilities:

$0.15 + 0.4 + 0.25 = 0.8$

So:

$0.8 + P(\text{yellow}) = 1$

$P(\text{yellow}) = 1 - 0.8 = 0.2$

$\boxed{P(\text{yellow}) = 0.2}$

Part (b): Probability of green

This value is read straight from the table; no calculation is needed:

$\boxed{P(\text{green}) = 0.25}$

Part (c): Probability of not blue

“Not blue” is the complement of “blue”. The probability of an event and the probability of it not happening also add to 1:

$P(\text{not blue}) = 1 - P(\text{blue}) = 1 - 0.4 = 0.6$

$\boxed{P(\text{not blue}) = 0.6}$

Alternative method (check): add the probabilities of all the other colours.

$P(\text{red}) + P(\text{green}) + P(\text{yellow}) = 0.15 + 0.25 + 0.2 = 0.6 \checkmark$

Both methods agree.

Part (d): Expected number of yellows in 200 spins

The expected number of times an outcome occurs is the probability of that outcome multiplied by the number of trials:

$\text{Expected yellows} = P(\text{yellow}) \times \text{number of spins} = 0.2 \times 200$

$0.2 \times 200 = 40$

$\boxed{\text{Expected number of yellows} = 40}$

This is an expected (theoretical) value; in a real experiment the actual number could be a little above or below 40.