Respuesta :
Answer:
a) [tex]P(Current year and last year)=0.15x0.09=0.0135=1.35\%[/tex]
b) [tex]P(Last year U Current year)=0.09+0.08-0.0135=0.1565=15.65\%[/tex]
Step-by-step explanation:
Conditional probability is the probability of one event occurring with some relationship to one or more other events.
The total probability rule (or the Law of Total Probability) breaks up probability calculations into distinct parts. P(AUB)=P(A)+P(B)-P(A and B)
The general multiplication rule formula is: P(A ∩ B) = P(A) P(B|A)=P(B)P(A|B)
We have the following probabilities:
[tex]P(Lastyear)=0.09=9\%[/tex]
[tex]P(Currentyear)=0.08=8\%[/tex]
[tex]P(Currentyear | Lastyear)=0.15=15\%[/tex]
Part a
We can use this multiplication rule:
[tex]P(A and B)=P(B|A)(A)=P(A|B)P(B)[/tex]
For this part we want this probability:
[tex]P(Current year and last year)=P(Current year|Last year)P(Last year)[/tex]
And if we replace we got:
[tex]P(Current year and last year)=0.15x0.09=0.0135=1.35\%[/tex]
Part b
For this part we want the probability of one event in last year OR one event on the current year, so we can use the probability addition of events:
[tex]P(AUB)=P(A)+P(B)-P(A and B)[/tex]
And for our case we have:
[tex]P(Last year U Current year) = P(Last year)+P(Current year)-P(Last year and Current year)[/tex]
[tex]P(Last year U Current year)=0.09+0.08-0.0135=0.1565=15.65\%[/tex]
Percentage of an amount is calculated as parts per cent(100).
- Total percent of the employees who will experience lost-time accidents in both years is: 1.35%
- Total percentage of the employees who will suffer at least one lost-time accidents over the two-year period is: 15.65%
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
((a/100) × b ) %
For the given case, let we have:
- Total number of employees = [tex]x[/tex]
- Percent of employees suffering lost-time accident in first year = 9%
- Percent of employees suffering lost-time accident in second year = 8%
Let we have:
A = Employees suffering lost-time accident in first year
n(A) = 9%
B = Employees suffering lost-time accident in second year
n(B) = 8%
Then, its given that:
A ∩ B = (employees suffering in both year from lost-time accidents).
n(A ∩ B ) = 15% of 9% = 15 × 9/100 = 1.35%
Thus, a) Total percent of the employees will experience lost-time accidents in both years is: 1.35%
Using Venn diagram's conclusion that:
n(A ∪ B) = n(A) + n(B) - n(A ∩B)
we get:
A ∪ B = Employees suffering from at least one lost-time accident(its either A or B or both)
Thus,
n(A ∪ B) = (9+8)% - 1.35% = 15.65%
Thus,
- Total percent of the employees who will experience lost-time accidents in both years is: 1.35%
- Total percentage of the employees who will suffer at least one lost-time accidents over the two-year period is: 15.65%
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