Teesha is in the French club. There are 22 students in the club. The French teacher will pick two students at random to guide visiting students from France. What is the probability that Teesha will not be picked as a guide?
Well, what is the probability that she WILL be one of the two?
1/22 + 1/21
so
1 - 1/22 - 1/21
Just realized what your teacher is getting at.
This is an "either or" problem, add
unlike the fish in the bowls where " this AND that" have to happen and you multiply
To find the probability that Teesha will not be picked as a guide, we first need to determine the total number of possible outcomes.
Since the French teacher will pick 2 students out of 22 students, the total number of possible outcomes can be calculated using combinations. The combination formula is given by:
nCr = n! / (r!(n-r)!)
Where n is the total number of students (22) and r is the number of students to be picked as guides (2).
Let's calculate the total number of possible outcomes:
nCr = 22! / (2!(22-2)!)
= 22! / (2!20!)
Calculating:
22! = 22 x 21 x 20! (22 factorial)
2! = 2 x 1 (2 factorial)
20! = 20 x 19 x 18 x ... x 2 x 1 (20 factorial)
Plugging these values into the equation:
nCr = (22 x 21 x 20!) / (2 x 1 x (20 x 19 x 18 x ... x 2 x 1))
= (22 x 21 x 20!) / (2!)
Simplifying further:
nCr = (22 x 21 x 20!) / 2
Now, let's determine the number of favorable outcomes, which is the number of ways that Teesha will not be picked as a guide.
Since Teesha is one of the 22 students, and only 2 students will be chosen, the number of favorable outcomes is given by:
Number of favorable outcomes = 21C2
Using the same combination formula:
nCr = n! / (r!(n-r)!)
We can calculate the number of favorable outcomes:
21C2 = 21! / (2!(21-2)!)
= 21! / (2!19!)
Calculating:
21! = 21 x 20!
2! = 2 x 1 (2 factorial)
19! = 19 x 18 x ... x 2 x 1 (19 factorial)
Plugging these values into the equation:
21C2 = (21 x 20!) / (2 x 1 x (19 x 18 x ... x 2 x 1))
= (21 x 20!) / 2
Simplifying further:
21C2 = (21 x 20!) / 2
Now, we can calculate the probability that Teesha will not be picked as a guide by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Substituting the values we calculated:
Probability = (21 x 20!) / 2 / [(22 x 21 x 20!) / 2]
Canceling out like terms:
Probability = 21 / 22
Therefore, the probability that Teesha will not be picked as a guide is 21/22 or approximately 0.9545.
To find the probability that Teesha will not be picked as a guide, we first need to determine how many possibilities there are for the French teacher to choose two students out of 22. This can be calculated using the combination formula, which is represented as "nCk" or "n choose k."
In this case, we have n = 22 (number of students) and k = 2 (number of students to be chosen as guides). So, the number of possibilities (nCk) can be calculated as:
22C2 = (22!)/(2!(22-2)!) = (22!)/(2!20!) = (22*21)/(2*1) = 231.
Now, to find the probability of Teesha not being picked, we need to determine the number of possibilities where Teesha is not chosen as one of the guides. This means considering the remaining 21 students (excluding Teesha) as potential candidates for the two guide positions. Thus, we calculate:
21C2 = (21!)/(2!(21-2)!) = (21!)/(2!19!) = (21*20)/(2*1) = 210.
Therefore, the probability that Teesha will not be picked as a guide is given by the number of possibilities where Teesha is not chosen divided by the total number of possibilities, as follows:
P(Teesha not picked) = 210/231 ≈ 0.909.
So, the probability that Teesha will not be picked as a guide is approximately 0.909 or 90.9%.