Trevor's soccer bag holds lots of socks: 4 red, seven green, three white, and two purple. He takes two socks, what is the probability that he will get red and green socks?
4+7+3+2 = 16 socks
prob red first = 4/16
prob green second = 7/15
prob that happens = (4*7)/(16*15)
prob green first = 7/16
prob red second = 4/15
so again (4*7)/(16*15)
so in the end 2 * 4 * 7 / (15*16)
= .233
To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the total number of ways Trevor can choose any two socks from his bag. To calculate this, we can use the combination formula, which is C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items we want to choose.
In this case, Trevor has a total of 4 red socks and 7 green socks. So we have n = 4 + 7 = 11 and r = 2. Plugging these values into the combination formula, we get:
C(11, 2) = 11! / (2!(11-2)!) = 11! / (2!9!) = (11 * 10 * 9!) / (2! * 9!) = (11 * 10) / (2 * 1) = 55
Therefore, there are 55 possible ways Trevor can choose any two socks from his bag.
Now let's determine the number of favorable outcomes, which is the number of ways Trevor can choose one red sock and one green sock. Trevor has 4 red socks and 7 green socks, so the favorable outcomes are the product of the number of red socks and the number of green socks:
Favorable outcomes = 4 * 7 = 28
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 28 / 55 = 0.509
Therefore, the probability that Trevor will get a red and a green sock is approximately 0.509 or 50.9%.