During a sale, 1/6 of the CD prices are reduced. Find the probability that 2 of 4 randomly-selected CDs have reduced prices.
How do I set this one up??
Thanks
C(4,2)*(1/6)^2*(5/6)^2
To set up this problem, we need to determine the total number of ways we can select 2 CDs with reduced prices out of the 4 randomly-selected CDs. Then, we need to find the total number of possible outcomes when selecting 4 CDs from the available CDs.
Let's break it down step by step:
Step 1: Determine the total number of ways to select 2 CDs with reduced prices.
Since 1/6 of the CDs have reduced prices, we can calculate the number of CDs with reduced prices:
Number of CDs with reduced prices = (1/6) * Total number of CDs
So, in this case, since we have 4 CDs, the number of CDs with reduced prices is:
Number of CDs with reduced prices = (1/6) * 4 = 2/3
Now, we need to calculate the number of ways to select 2 CDs from the 2 CDs with reduced prices. This is a combination problem, which can be calculated using the combination formula:
Number of ways to select 2 CDs with reduced prices = (Number of CDs with reduced prices) C (Number of CDs to be selected)
= (2/3) C 2
= [(2/3)!] / [(2 - 2)! * 2!]
= (2/3 * 1/3) / (1 * 2)
= 1/3
Step 2: Determine the total number of possible outcomes when selecting 4 CDs from the available CDs.
Since we have 4 CDs in total, the number of possible outcomes when selecting 4 CDs can be calculated using the combination formula:
Number of possible outcomes = (Total number of CDs) C (Number of CDs to be selected)
= 4 C 4
= [(4)!] / [(4 - 4)! * 4!]
= (4 * 3 * 2 * 1) / (1 * 2 * 3 * 4)
= 1
Step 3: Calculate the probability.
The probability of selecting 2 CDs with reduced prices out of 4 randomly-selected CDs can be calculated by dividing the number of ways to select 2 CDs with reduced prices by the total number of possible outcomes:
Probability = (Number of ways to select 2 CDs with reduced prices) / (Number of possible outcomes)
= (1/3) / 1
= 1/3
Therefore, the probability that 2 of the 4 randomly-selected CDs have reduced prices is 1/3.