SURENDRA K. answered • 07/13/14

An experienced,patient & hardworking tutor

Maaria Z.

asked • 03/13/13I have this question regarding set theory and probability that i am struggling on:

Q: A group of international students take part in a survey on the nationality of their parents.

E= English Parent

F= French parent

n(ξ) = 50, n(E) = 15, n(F )= 9, n(E U F)' = 33

**(1) Find n(E ∩ F) **

** (2) Find n(E' U F)**

** (3) A student is chosen at random. Find the probability that this student has an English parent and a French parent.**

**(4) A student who has a French parent is chosen at random. Find the probability that this student also has an English parent.**

** **

**Thankyou so much for any help ! **

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SURENDRA K. answered • 07/13/14

An experienced,patient & hardworking tutor

Q1 The above answer is correct.

Q2 The answer is not correct.

It is 21/25. or 42/50

Q3 The correct answer is 7/50

Q4. Q 4 is same as Q3.No different.

Surendra

Luke B. answered • 03/13/13

fun + learning = inevitable progress

First thing to do is draw a Venn diagram. It will help tremendously.

If n(E U F)' = 33, then n(E U F) = 50 - 33 = 17, because n(E U F) + n(E U F)' = n(total).

We also know that n(E U F) = n(E) + n(F) - n(E ∩ F). Substitute values to get 17 = 15 + 9 - n(E ∩ F). Solve for n(E ∩ F) and get n(E ∩ F) = 7.

n(E' U F) is the number of students without an English parent plus the number of students with a French parent, which is the total number of students minus the number with an English parent, plus the number with a French parent: n(total) - n(E) + n(F) = 50 - 15 + 9 = 44.

Probability of a student with an E and and F is the probability of the union of E and F.

For the last one, it will be the intersection of E and F. I highly recommend you draw a Venn diagram and work this through!

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Maaria Z.

Thankyou so much.

03/13/13