Question

1 Vicky has a collection of medals.

The Venn diagram gives information about the number of medals in her
collection where
8 = {all medals}
A = {English medals}
B = {gold medals}
E
7x-11
x
5x-3
34
B
Vicky is going to take at random a medal from her collection.
Given that the medal is gold, the probability that the medal is English is
11
Work out the number of medals in Vicky's collection.

PLEASE HELPPPPP

Answer 1

To find the number of medals in Vicky's collection, we can use the formula for finding the number of elements in a universal set. Given that the probability that the medal is English when it is gold is 11, we can find the sum of A and B to determine the number of medals.

To find the number of medals in Vicky's collection, we need to determine the number of elements in the set 8. We can use the formula for finding the number of elements in a universal set:

|8| = |A| + |B| - |A∩B|

Given that the probability that the medal is English when it is gold is 11, we know that the number of English gold medals (A∩B) is 11.

Substituting the known values into the formula:

|8| = |A| + |B| - 11

We also know that A = |A|, B = |B|, and |8| = 8. Substituting these values into the equation:

8 = A + B - 11

Now, we can solve for the number of medals, which is the sum of A and B:

A + B = 19

Therefore, the number of medals in Vicky's collection is 19.