Question

Your sock drawer has two white socks,six brown socks,and six black socks.You randomly pick a sock and put on your left foot and then pick another sock and put it on your right foot. You randomly grab two socks out of the drawer to put on. What are the odds that you first grab a white sock, and then you grab a brown sock?

Answer 1

The odds of first grabbing a white sock and then a brown sock are calculated by multiplying the individual probabilities of each event occurring in sequence. The final odds are 6 in 91.

Step-by-step explanation:

The question involves calculating the probability of selecting socks of certain colors in a specific order from a drawer. To find the odds that you first grab a white sock, and then grab a brown sock, we need to use the concept of conditional probability since the events are dependent (not replacing the first sock affects the outcome of the second draw).

First, we calculate the probability of drawing a white sock. There are 2 white socks out of a total of 14 (2 white + 6 brown + 6 black). The probability is therefore 2/14 or 1/7.

Next, we calculate the probability of drawing a brown sock given that the first sock drawn was white. Now there are 6 brown socks left out of the remaining 13 socks (since one white sock has already been taken). The probability is 6/13.

To find the overall probability of both events happening in sequence, we multiply the probabilities of each event: (1/7) * (6/13) = 6/91.

Therefore, the odds of first grabbing a white sock and then grabbing a brown sock are 6 in 91.