0.4857
Sock Color Probability: 0.486
User
Please Answer: This Is Probability: There are six grey socks and nine white socks in a drawer. Jake randomly picks out two socks, without replacement, to wear.
A.) Draw a tree diagram to represent all possible outcomes and the corresponding possibilities. ( I have already answered A.)
B.) What is the probability that Jake will pick out two socks of the same colour?
ChatGPT
To determine the probability that Jake will pick out two socks of the same color, we need to calculate the favorable outcomes (when both socks are either grey or white) and divide it by the total number of possible outcomes.
Total number of socks = 6 grey socks + 9 white socks = 15 socks
Since Jake picks two socks without replacement, the total number of possible outcomes is given by the combination formula:
Total possible outcomes = C(15, 2) = 15! / (2!(15-2)!) = 15! / (2! * 13!) = (15 * 14) / (2 * 1) = 105
Next, we calculate the number of favorable outcomes, which is when both socks are either grey or white. There are two cases to consider:
Case 1: Jake picks two grey socks
Number of grey socks = 6
Possible outcomes when two grey socks are picked = C(6, 2) = 6! / (2!(6-2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15
Case 2: Jake picks two white socks
Number of white socks = 9
Possible outcomes when two white socks are picked = C(9, 2) = 9! / (2!(9-2)!) = 9! / (2! * 7!) = (9 * 8) / (2 * 1) = 36
Now we can calculate the total number of favorable outcomes:
Total favorable outcomes = Number of favorable outcomes for case 1 + Number of favorable outcomes for case 2 = 15 + 36 = 51
Finally, we can calculate the probability by dividing the favorable outcomes by the total possible outcomes:
Probability of picking two socks of the same color = Total favorable outcomes / Total possible outcomes = 51 / 105 ≈ 0.4857 (rounded to four decimal places)