Answer: If replaced: 0.075 or 7.5%
If not replaced: 0.00455 or 0.455%
Explanation:
If the diamonds are replaced after each draw:
The probability of drawing a real diamond is 9/12, found by making the numerator the number of real diamonds and adding the total number of diamonds to find the denominator. 3+9 = 12.
9/12 can be reduced to 3/4 by dividing the numerator and denominator by 3.
To find the probability of all 9 diamonds drawn being real, multiply 3/4 by itself 9 times.
= 19683.
= 262144. This creates a probability of 19683/262144. This cannot be reduced because there is no common factor. To express as a decimal, divide. 19683/262144 = 0.07508. To turn this into a percent, multiply by 100. 0.07508*100 = 7.508
If the diamonds are not replaced after each draw:
Start with the probability of drawing a single diamond: 9/12. After each draw, both the numerator and denominator have 1 subtracted from them, since there is 1 less real diamond and 1 less diamond in total. This will give you the equation (9/12)*(8/11)*(7/10)*(6/9)*(5/8)*(4/7)*(3/6)*(2/5)*(1/4). This equals 0.00455. To find as a percent, multiply by 100. 0.00455*100 = 0.455