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 will not have to work, in addition to Monday.
One week Abia gets to draw her two days first.
a) What is the conditional probability that Abia will draw a second weekend day, given that her first draw was a weekend day?
b) What is the probability that Abia will get to enjoy a three-day weekend (Saturday to Monday)?
a) 1/5
b) 1/6 + 1/5 = ?
a) Ah, the thrilling world of slip drawing! Let's calculate the conditional probability for Abia. The first draw has already been completed, and it was a weekend day. Now, there are four days remaining in the hat: Tuesday, Wednesday, Thursday, and Friday. Two of these days are weekend days. So, the probability of drawing a second weekend day is 2 out of 4, which simplifies to 1 out of 2 or 0.5. Therefore, the conditional probability that Abia will draw a second weekend day, given that her first draw was a weekend day, is 0.5.
b) Ah, the dream of a three-day weekend! In order for Abia to enjoy a three-day weekend from Saturday to Monday, both of her draws need to be on these days. The first draw has a 2 out of 7 chance of being a Saturday, and the second draw has a 1 out of 6 chance of being a Monday. Multiplying these probabilities together, we get 2/7 * 1/6 = 1/21. So, the probability that Abia will get to enjoy a three-day weekend is 1 out of 21, or approximately 0.048. Keep your fingers crossed for Abia!
To solve this problem, let's analyze the different possibilities:
4 weekend days (Saturday and Sunday)
3 non-weekend days (Tuesday, Wednesday, Thursday)
a) What is the conditional probability that Abia will draw a second weekend day, given that her first draw was a weekend day?
Since Abia's first draw was a weekend day, there are 4 remaining weekend days and 4 remaining non-weekend days. Therefore, the probability of drawing a second weekend day is:
P(Drawing a second weekend day | First draw was a weekend day) = 4/8 = 1/2
b) What is the probability that Abia will get to enjoy a three-day weekend (Saturday to Monday)?
To get a three-day weekend (Saturday to Monday), Abia must draw Saturday or Sunday as her first day off and draw Monday as her second day off. We need to calculate the probability of both events happening.
The probability of drawing Saturday or Sunday as the first day off is 4/8, since there are 4 weekend days out of 8 total days.
Given that the first day off is a weekend day, the probability of drawing Monday as the second day off is 3/7, since there are 3 remaining non-weekend days out of 7 remaining total days.
Therefore, the probability of Abia getting a three-day weekend is:
P(Three-day weekend) = P(Drawing a weekend day as first day off) * P(Drawing Monday as second day off) = (4/8) * (3/7) = 12/56 = 3/14
To solve these probability problems, we need to determine the sample space and the favorable outcomes.
Let's start by identifying the sample space for Abia's draws. Since Abia draws two slips of paper, there are a total of 7 possible outcomes, which correspond to the days of the week (Tuesday to Sunday and Monday).
a) Conditional Probability:
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 determine the favorable outcomes and divide it by the total number of outcomes.
Favorable outcomes: Abia must draw a weekend day on the first draw (Sunday or Saturday) and then draw another weekend day on the second draw.
There are 2 favorable outcomes: (Saturday, Saturday) and (Sunday, Sunday).
Total outcomes are 7.
Therefore, the conditional probability is 2/7.
b) Probability of a Three-Day Weekend:
To calculate the probability that Abia will enjoy a three-day weekend (Saturday to Monday), we need to determine the favorable outcomes and divide it by the total number of outcomes.
Favorable outcomes: Abia needs to draw both Saturday and Monday.
There is only 1 favorable outcome: (Saturday, Monday).
Total outcomes are still 7.
Therefore, the probability of Abia getting a three-day weekend is 1/7.