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 [tex]=^{1000}C_{100}[/tex]
Number of sapphires = 300
We have to select 100 out of 300 sapphires .
So, the favorable outcomes [tex]=^{300}C_{100}[/tex]
Now,
[tex]\text{Required probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]\text{Required probability}=\dfrac{^{300}C_{100}}{^{1000}C_{100}}[/tex]
Therefore, the required probability is [tex]\dfrac{^{300}C_{100}}{^{1000}C_{100}}[/tex].
