Question

Mike is looking at different types of racks at a home improvement store. The store has: 8 coat racks11 key racks 16 shoe racks 5 utility racks Which situation would have a probability of 27/40?A.) Mike picking a utility or coat rack B.) Mike picking a key or shoe rackC.) Mike picking a utility or shoe rack D.) Mike picking a key or coat rack.

Answer 1

The store has:

8 coat racks

11 key racks

16 shoe racks

5 utility racks

Total number of racks = 8 +11+16 +5

Total number of racks=40

Probability is define as the ratio of number of favourable outcomes to the number possible outcomes

$\text{ Probability=}\frac{Number\text{ of favourable Outcomes}}{Total\text{ number of outcomes}}$

A) Mike picking a utility or coat rack

i,e Probability of 5 utility or 8 coat rat;

$\begin{gathered} \text{Probability of a utility or coat rack=}\frac{Number\text{ of Utility}}{Total\text{ number of racks}}+\frac{Number\text{ of coat racks}}{Total\text{ number of racks}} \\ \text{Probability of a utility or coat rack=}\frac{5}{40}+\frac{8}{40} \\ \text{Probability of a utility or coat rack=}\frac{13}{40} \end{gathered}$

B) Mike picking a key or shoe rack

Probability of 11 key racks or 16 shoe racks

$\begin{gathered} \text{ Probability of key racks or shoe racks=}\frac{Number\text{ of key raks + number of shoe racks}}{Total\text{ number of racks}} \\ \text{Probability of key racks or shoe racks=}\frac{11+16}{40} \\ \text{Probability of key racks or shoe racks=}\frac{27}{40} \end{gathered}$

Thua, the proability will be 27/40 if Mike picking a key or shoe rack



Answer : B) Mike picking a key or shoe rack