Answer: a) 8 b(i)) 19/55 b(ii)) 28/55
Step-by-step explanation:
To get the answer to B you add all of the numbers in the venn diagram which gives you 47 and then you subtract that from the overall number of students which gives you 8.
To find the number of students who passed french and german you take the number from the middle of the diagram (19) and put it out of the overall number of students which is 55 and so the answer is 19/55
To find the number of students that passed exactly one of these two subjects you put 17/55 (those who passed french) and 11/55 (those who passed german) and then you add them together which gives you 28/55.
The number of students that did not pass either subjects is 8.
The probability of that a student passed both French and German is 19/55.
The probability that a student passed exactly one of these two subjects is 28/55.
A Venn diagram is a pictorial representation of sets. It is made up of circles that are enclosed in a rectangle. The number that intersects the circles is common to both elements.
In the given Venn diagram, the number that is not in the circle represents the number of students that did not pass either the French nor German exam.
Number of students that did not pass either subjects = number of students - (number of students that passed the French exam + number of students that passed the German exam + number of students that passed both subjects)
55 - (17 + 19 + 11)
55 - 47
= 8 students
The number of students that passed both subjects is represented by the number that is at the intersection of both circles. The number is 19.
The probability of that a student passed both French and German = number of students that passed both French and German / total number of students
= 19 / 55
The probability that a student passed exactly one of these two subjects = fraction of students that passed French + fraction of students that passed German
11/55 + 17/55 = 28/55
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