a sock drawer contains 10 white socks, 6 black socks, and 8 blue socks.
if 2 socks are chosen at random, what is the probability of getting a pair of white socks?
To find the probability of getting a pair of white socks, we first need to determine the total number of possible pairs of socks that can be chosen.
The total number of socks in the drawer is 10 white socks + 6 black socks + 8 blue socks = 24 socks.
To find the total number of possible pairs, we can use the combination formula (nCr) where n represents the total number of socks and r represents the number of socks being chosen in each pair. In this case, we are choosing 2 socks, so r = 2.
Using the combination formula, the total number of possible pairs can be calculated as:
24C2 = (24!)/(2!(24-2)!) = (24!)/(2!22!) = (24x23)/(2x1) = 276.
Now, we need to determine the number of pairs of white socks that can be chosen. Since there are 10 white socks in the drawer, we can use the combination formula again:
10C2 = (10!)/(2!(10-2)!) = (10!)/(2!8!) = (10x9)/(2x1) = 45.
Therefore, the number of pairs of white socks that can be chosen is 45.
Finally, we can calculate the probability of getting a pair of white socks by dividing the number of pairs of white socks by the total number of possible pairs:
Probability = Number of pairs of white socks / Total number of possible pairs
= 45 / 276
= 0.163, rounded to 3 decimal places.
So, the probability of getting a pair of white socks is approximately 0.163 or 16.3%