Abia is one of three servers who work at a restaurant that is open from tuesday to sunday.
Every week the servers randomly draw slips of paper from a hat to decide which two days they won't have to work, in addition to monday.
What is the conditional probability that Abia will draw a second weekend day, given that her first draw was a weekend day?
I did (2/6)(1/5) and that's 1/15 but the answer is 1/20. Please help!!!!
Your answer is right
To solve this problem, we need to break it down step by step.
First, let's determine the total number of possible outcomes when Abia draws her first weekend day. There are 2 weekend days out of 6 total days in a week, so the probability of drawing a weekend day on the first draw is 2/6.
Next, we need to consider the remaining days that Abia can draw for her second day off. After drawing the first weekend day, there are now only 5 days left in the hat. However, since we want to find the probability of Abia drawing a second weekend day, we need to consider that there is only 1 remaining weekend day out of those 5 days. So, the probability of drawing a second weekend day is 1/5.
Finally, to find the conditional probability (the probability of drawing a second weekend day given that the first draw was a weekend day), we multiply the probabilities of drawing a weekend day on the first and second draws. Therefore, the conditional probability is (2/6) * (1/5) = 2/30 = 1/15.
It seems that your calculation is correct. However, the provided answer of 1/20 does not match the calculations. It's possible that there was a mistake in the answer key or in the source where you obtained the answer. I would recommend double-checking the original problem and the answer you were given.
To calculate the conditional probability that Abia will draw a second weekend day, given that her first draw was a weekend day, we need to take into account the total number of days and the number of weekend days.
In a week, there are 7 days (Tuesday to Sunday). Out of these 7 days, 2 are weekend days (Saturday and Sunday).
So, when Abia makes her first draw, there is a 2/7 probability of drawing a weekend day.
Now, if she has already drawn a weekend day, there are 6 days remaining, out of which 1 is a weekend day.
Therefore, the probability of drawing a second weekend day, given that the first draw was a weekend day, is equal to (2/7) * (1/6) = 1/21.
Hence, it appears that the correct calculation should be 1/21, not 1/20.