Annie and her fiends started a club. The Venn diagram shows information about the 16 members of the club.

Part A: A randomly selected club member is a junior and a girl.

Part B: A randomly selected club member is not a junior girl.

Part C: A randomly selected club member is a junior or a girl. Use the formula
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Then according to given venn diagram lets donate juniors as A and girls as B. As it is given that there are 16 members and there are only 3 members in the overlapped section of venn diagram.

So, probability of randomly Selected club member is junior and a girl is

P(A∩B) = 3/16.

∴ The probability of randomly Selected club member is junior and a girl is 3/16

Part B :

A randomly selected club member is not a junior girl is 1/4.

To find the probability of randomly selecting a member who is not a junior girl, we have to find compliment of two events (junior and a girl) which is a part that is outside the both circles of venn diagram U. So we can see that there are only 4 members outside the venn diagram A and B and there are total of 16 members . So probability of randomly selected club member is not a junior girl is

P(U) = 4/16

⇒ P(U) = 1/4.

∴ The probability of randomly selected club member is not a junior girl is 1/4.

Part C :

From the diagram is shown that number of members of juniors A = 7

So, we can find the probability to randomly select a junior is P(A) = 7/16

Similarly number of members of girls B = 8/16

So, probability to randomly select a girl is P(b) = 8/16

∴To find P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A ∪ B) = 7/16 + 8/16 - 3/16

⇒ P(A ∪ B) = 15/16 - 3/16

⇒ P(A ∪ B) = 12/16

⇒ P(A ∪ B) = 3/4

The probability of randomly Selected club member is junior and a girl is 3/4.

A randomly selected club member is not a junior girl is 1/4.

P(A ∪ B) = 3/4

To read more about venn diagram :

https://brainly.com/question/1402647

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