Question

Lisa finds a treasure chest full of 1000 jewels: 600 emeralds, 300 sapphires, and 100 rubies. She stuffs her pockets full of jewels completely at random, but they can only hold 100 jewels. What is the probability that all 100 jewels she took were sapphires?

Answer 1

Given:

Total number of jewels = 1000

Emeralds = 600

Sapphires = 300

Rubies = 100 rubies

100 jewels she took randomly.

To find:

The probability that all 100 jewels she took were sapphires.

Solution:

Number of selected jewels = 100

Total number of jewels = 1000

We have to select 100 out of 1000.

So, the total number of outcomes
`=^(1000)C_(100)`

Number of sapphires = 300

We have to select 100 out of 300 sapphires .

So, the favorable outcomes
`=^(300)C_(100)`

Now,

`\text{Required probability}=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}`

`\text{Required probability}=(^(300)C_(100))/(^(1000)C_(100))`

Therefore, the required probability is
`(^(300)C_(100))/(^(1000)C_(100))`.