Question

Of 24 employees at a local supermarket, 13 work as cashiers and 11 stock shelves. If 4 employees are selected at random to work overtime, determine the probability that all 4 are cashiers.

Answer 1

Answer:
`(65)/(996)`

Explanation:

Given : Total number of employees = 24

Number of cashiers = 13

Number of stock shelves = 11

Number of ways to choose 4 out of 24 people =
`^(24)C_4` (Total outcomes)

Number of ways to select 4 out of 13 cashiers =
`^(13)C_(4)` (Favorable outcomes)

According to the definition of probability :
`\frac{\text{Favorable outcomes}}{\text{Total outcomes}}`

Then , the probability that all selected 4 employees are cashiers. :-

`(^(13)C_4)/(^(24)C_(4))\\\\=((13!)/(4!9!))/((24!)/(4!20!))\\\\=(65)/(996)`

Hence, the required probability is
`(65)/(996)` .

Answer 2

The required probability is,
`\simeq 0.06729`

Explanation:

Of 24 employees at a local supermarket, 13 work as cashiers and 11 stock shelves. If 4 employees are selected at random to work overtime, then

P( all 4 are cashiers) =
`\frac{^(13){C}_(4)}{^(24){C}_(4)}`

`\simeq 0.06729`