Every hour of training raises the salary
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Part a)
Identify the variable and categories
By reading the above statement, we can find that there are two variables and each variable has 2 categories. The variables and their categories are:
1) Class Number
This variable is further divided into 2 categories i.e. Class 9th and Class 10th.
2) Participation in Extracurricular activities
This variable is further divided into 2 categories based on if students participated or not.
Part b)
Set up and fill 2 way table.
Since, we have 2 variables and each variable has 2 categories the number of data cells will be 2 x 2 = 4 cells
There are total 100 students. 40 students are in class 10th. This means 60 students are in class 9th.Out of 40 students in class 10th, 18 students participate in at least one extracurricular activity. So remaining 22 students do not participate. 32 students from class 9th participate in extracurricular activities, this means the remaining 28 students do not participate. Based on this data, we can fill up the table as shown below
Identify the variable and categories
By reading the above statement, we can find that there are two variables and each variable has 2 categories. The variables and their categories are:
1) Class Number
This variable is further divided into 2 categories i.e. Class 9th and Class 10th.
2) Participation in Extracurricular activities
This variable is further divided into 2 categories based on if students participated or not.
Part b)
Set up and fill 2 way table.
Since, we have 2 variables and each variable has 2 categories the number of data cells will be 2 x 2 = 4 cells
There are total 100 students. 40 students are in class 10th. This means 60 students are in class 9th.Out of 40 students in class 10th, 18 students participate in at least one extracurricular activity. So remaining 22 students do not participate. 32 students from class 9th participate in extracurricular activities, this means the remaining 28 students do not participate. Based on this data, we can fill up the table as shown below
Answer:
(a) 0.0256
(b) 0.2944
Step-by-step explanation:
For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:
Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.
Additionally, nCx is calculated as:
So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.
Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:
P(2,2,0.16)=0.0256
For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.
Using the same equation to calculate P(1,2,0.16) we get:
P(1,2,0.16)=0.2688
So, the probability that at least one person is allergic to pollen is 0.2944 and it is calculated as:
0.0256 + 0.2688 = 0.2944