[SOLVED]-aux.17 Venn diagram

karush

Well-known member
IB24
1202
2000
(a) $E\cup H = 88-39=49$ and since $32+28=60$ then $b=60-49= E\cap H = 11$
so $a=32-11=21$ and $c=28-11=17$

hope this ok before (b) and (c)

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MarkFL

Staff member
I get the same results as you. I wrote:

$$\displaystyle a+b=32$$

$$\displaystyle b+c=28$$

$$\displaystyle a+b+c=49$$

and solved the system.

karush

Well-known member
(b)(I) $\frac{11}{88}=\frac{1}{8}$
(b)(ii) $\frac{56}{88}=\frac{7}{11}$

MarkFL

Staff member
i) Correct.

ii) Incorrect. Given that he studies economics means the denominator is $a+b=32$. If he does not study history, then the numerator is $a=21$.

eddybob123

Active member
c)

i) Find the probability that one student does not study economics and then cube the result
ii) Note that this is mutually independent from part i).

karush

Well-known member
c)
1(i) Find the probability that one student does not study economics and then cube the result ii) Note that this is mutually independent from part i).
(i) $\displaystyle(\frac{56}{88})^3=\frac{343}{1331}$

eddybob123

Active member
(i) $\displaystyle(\frac{56}{88})^3=\frac{343}{1331}$ Did you do part ii)?

karush

Well-known member Did you do part ii)?
(C)(ii) in that the probability of just one student to take economics is $\displaystyle\frac{32}{88}$ i would presume that since $3$ students are randomly picked that $3x$ this would be the probability for at least one of these students to be in the econ class which would be $\displaystyle\frac{96}{88}$ which is more than a $100\%$

I was trying to do this with a cell phone yesterday and it took forever....but now on PC

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eddybob123

Active member
(C)(ii) in that the probability of just one student to take economics is $\displaystyle\frac{32}{88}$ i would presume that since $3$ students are randomly picked that $3x$ this would be the probability for at least one of these students to be in the econ class which would be $\displaystyle\frac{96}{88}$ which is more than a $100\%$

I was trying to do this with a cell phone yesterday and it took forever....but now on PC
i) and ii) are mutually independent and together represents the whole sample space. You don't need to do calculations to part ii) separately. Just take the result from i) and subtract it from 1.

karush

Well-known member
i) and ii) are mutually independent and together represents the whole sample space. You don't need to do calculations to part ii) separately. Just take the result from i) and subtract it from 1.
$\frac{988}{1331}$