there were 6 purple socks and 4 orange socks in a drawer. Zucky picked one sock without looking(or replacing the first). What is the probability that he picked 2 purple socks?
prob (purple, purple) = (6/10)(5/9) = 1/3
3/10
To find the probability that Zucky picked 2 purple socks, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes can be found by calculating the total number of ways Zucky can choose any two socks from the 10 socks in the drawer. This can be calculated using combinations.
The formula for combinations is: nCr = n! / (r! * (n-r)!)
Where n is the total number of items, r is the number of items to be chosen, and the ! represents factorial.
In this case, n = 10 (total number of socks) and r = 2 (number of socks Zucky needs to pick).
Using the combination formula, we can calculate the total number of possible outcomes:
10C2 = 10! / (2! * (10-2)!) = 45
Now let's determine the number of favorable outcomes, which is the number of ways Zucky can pick 2 purple socks. We have 6 purple socks in the drawer, so the number of ways Zucky can pick 2 purple socks can be calculated using combinations again.
In this case, n = 6 (number of purple socks) and r = 2 (number of socks Zucky needs to pick).
Using the combination formula, we can calculate the number of favorable outcomes:
6C2 = 6! / (2! * (6-2)!) = 15
Finally, to find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 15/45 = 1/3
Therefore, the probability that Zucky picked 2 purple socks is 1/3 or approximately 0.3333.