Answer: 0.2899
Step-by-step explanation:
1. Find total number of ways to chose 4 rocks out of 32 rocks (total)
C(32,4)
2. Find number of ways to choose 2 sedimentary rocks out of 10 sedimentary rocks out of the remaining 22 non-sedimentary rocks (12 igneous + 10 metamorphic)
Number of ways to choose 2 sedimentary out of 10 sedimentary rocks=C(10,2)=45
umber of ways o choose 2 non-sedimentary out of 22 non-sedimentary rocks=C(22,2)=231
3. Multiply these two numbers together to get total number of favorable outcomes then divide by total number of possible outcomes to get probability
(C(10,2)*C(22,2))/C(32,4)
C(n,k)=n!/(k!*(n-k)!)
C(n,k) reprises the number of combinations of choosing k items from n items
C(10, 2) = 10! / (2! * (10 - 2)!)
= 45
C(22, 2) = 22! / (2! * (22 - 2)!)
= 231
C(32, 4) = 32! / (4! * (32 - 4)!)
= 35960
Now, substitute these values into the probability formula:
Probability = (45 * 231) / 35960
≈ 0.2899
