Your drawer contains 7 red socks and 6 blue socks. It's too dark to see the color of the socks, so you randomly pull two socks from the drawer. What is the probability that both socks are blue?
prob(2 blue) = (6/13)(5/12) = 5/26
A more interesting question would have been:
What is the least number of sox he would have to pull, before he has a matching pair ?
Well, let's do some sock math! If you have 7 red socks and 6 blue socks, that makes a total of 13 socks. When you randomly pull out one sock, there are now 12 socks left in the drawer. Since you want to pick two blue socks in a row, you'll want to calculate the probability of picking a blue sock first, which is 6 out of 12. Then, once you've picked that blue sock, there are 11 socks remaining in the drawer, with 5 of them being blue. So, the probability of picking a second blue sock is 5 out of 11. Now, to find the probability of both events happening together, you multiply the two probabilities: (6/12) * (5/11), which simplifies to 30/132. Therefore, the probability of randomly pulling out two blue socks is approximately 0.227 or 22.7%. Good luck with your sock adventures!
To find the probability that both socks are blue, we need to determine the total number of possible outcomes (sample space) and the number of favorable outcomes.
Total number of possible outcomes (sample space):
When randomly pulling two socks from the drawer without replacement, there are a total of 13 socks that can be selected (7 red + 6 blue).
Number of favorable outcomes:
To select two blue socks, we need to choose 2 socks from the 6 available blue socks, which can be done in C(6, 2) ways (denoted as 6C2 or "6 choose 2") using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
C(6, 2) = 6! / (2! * (6 - 2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15
Probability of both socks being blue:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes:
P(both socks are blue) = Number of favorable outcomes / Total number of possible outcomes
P(both socks are blue) = 15 / 13
Hence, the probability that both socks randomly pulled from the drawer are blue is 15/13 or approximately 1.154.
To find the probability that both socks are blue, you need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When you randomly pull two socks from the drawer, there are a total of 13 socks in the drawer, so the number of possible outcomes is 13C2, which means choosing 2 socks out of 13.
Number of favorable outcomes:
Since there are 6 blue socks in the drawer, the number of ways to choose 2 blue socks out of 6 is 6C2.
Applying the formula for probability:
The probability of an event A occurring is given by P(A) = (Number of favorable outcomes) / (Total number of possible outcomes).
Therefore, the probability that both socks are blue can be calculated as:
P(Both socks are blue) = (Number of favorable outcomes) / (Total number of possible outcomes) = 6C2 / 13C2.
Now, let's calculate the probability using the combination formula:
6C2 = (6!)/(2!(6-2)!) = (6!)/(2!4!) = (6x5x4!)/(2x1x4!) = (6x5)/(2x1) = 15.
13C2 = (13!)/(2!(13-2)!) = (13!)/(2!11!) = (13x12)/2 = 78.
P(Both socks are blue) = 15/78 ≈ 0.1923.
Hence, the probability that both socks are blue is approximately 0.1923 or 19.23%.