There are 6 gray socks,8 brown socks and 2 blue socks in a drawer.If you remove 2 socks without looking,what is the probability that they are both blue?
well, what is the chance that the 1st sock is blue?
Having removed it, what is the chance that the 2nd is blue? The number of blues and the number of socks have both been changed by removing the 1st blue sock.
Now just multiply.
To find the probability that both socks are blue, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of ways to choose any 2 socks from the total number of socks in the drawer. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
where C(n, r) represents the number of combinations of choosing r items from a set of n items.
In this case, the total number of possible outcomes is calculated as C(16, 2), which is equal to:
C(16, 2) = 16! / (2!(16-2)!) = 16! / (2! 14!) = (16 * 15) / (2 * 1) = 120
Now, let's determine the number of favorable outcomes, i.e., the number of ways to choose 2 blue socks from the 2 blue socks available. Since there are only 2 blue socks, the number of favorable outcomes is 1 (choosing both blue socks).
Therefore, the probability of choosing 2 blue socks is:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 1 / 120
Probability = 0.0083 (rounded to four decimal places)
Hence, the probability that both socks are blue is approximately 0.0083 or 0.83%.