Your drawer contains 11 red socks and 6 blue socks. It's too dark to see which are which, but you need a pair of socks so you grab two. What is the probability that both socks are red?
17 total socks, so P(red,red) = 11/17 * 10/16 = _____
To find the probability that both socks are red, we need to calculate the ratio of the number of favorable outcomes (both socks are red) to the total number of possible outcomes.
In this scenario, there are 17 total socks in the drawer, 11 of which are red and 6 of which are blue. Since you randomly grab two socks without looking, there are two possible favorable outcomes: selecting a red sock followed by another red sock.
To compute the probability, we can use the formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Number of favorable outcomes = 11 red socks choose 2 = 11C2 = (11 * 10) / (2 * 1) = 55
Total number of possible outcomes = 17 socks choose 2 = 17C2 = (17 * 16) / (2 * 1) = 136
Probability = 55 / 136 = 0.4044 (rounded to four decimal places)
Therefore, the probability that both socks drawn will be red is approximately 0.4044 or 40.44%.