Sarita works 2 days each week. If her office is open 7 days each week, use pascal's triangle to find the probability that she will be scheduled for Wednesday and Saturday next week.
A. 2/7
B. 1/14
C. 1/21
D. 1/42
What are the coording of the vertice a,b,c,d,e,f,g,of the shape below
Please draw a number line from -7 to+7 on the line and mark the pointr a(6)b(5)c(-4)d(-6)e(5)
To find the probability that Sarita will be scheduled for Wednesday and Saturday next week, we need to determine the number of ways she can be scheduled for those two days, and then divide that by the total number of possibilities.
First, let's look at Pascal's Triangle. Pascal's Triangle is a triangular array of numbers in which each number is the sum of the two directly above it. Each row represents the coefficients of the binomial expansion.
The first few rows of Pascal's Triangle look like this:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
....
To find the number of ways Sarita can be scheduled for Wednesday and Saturday, we need to look at the coefficients of the binomial expansion. In this case, we need to look at the fifth row of Pascal's Triangle because we have two days to choose from (Wednesday and Saturday) out of seven days in total (from Monday to Sunday).
The fifth row of Pascal's Triangle is:
1 4 6 4 1
The coefficients in this row represent the number of ways to select a specific number of days out of the total number of days (7).
In this case, we want to find the number of ways to select Wednesday and Saturday out of the seven days. Looking at the coefficients, we can see that the third coefficient (6) represents the number of ways to select two days out of seven.
Therefore, the number of ways Sarita can be scheduled for Wednesday and Saturday is 6.
The total number of possibilities is the total number of ways Sarita can be scheduled for any two days out of the seven days, which is the sum of all the coefficients in the fifth row of Pascal's Triangle: 1 + 4 + 6 + 4 + 1 = 16.
To find the probability, we divide the number of ways Sarita can be scheduled for Wednesday and Saturday (6) by the total number of possibilities (16):
Probability = 6/16
Simplifying the fraction, we get:
Probability = 3/8
Therefore, none of the given answer choices match the probability.