The Student Room Group

Stats 1

In a school of 400 pupils, 250 play a musical instrument and 100 sing in the choir.

The probability that a pupil chosen at random neither plays a musicla instrument nor sings in the choir is 1/5.

i)How many pupils both sing in the choir and play a musical instrument?
ii)Find the probability that a puipil chosen at random sings in the choir but does not play an instrument
iii)Find the probability that member of the choir chosen at random does not play an instrument
iv)Find the probability that someone who does not play an instrument chosen at random, is in the choir.

I really don't get any of this, mainly because I'm not sure how this is supposed to be a question of Conditional Probability. Please help! thanks
Reply 1
Strange Dog
In a school of 400 pupils, 250 play a musical instrument and 100 sing in the choir.

The probability that a pupil chosen at random neither plays a musicla instrument nor sings in the choir is 1/5.

i)How many pupils both sing in the choir and play a musical instrument?
ii)Find the probability that a puipil chosen at random sings in the choir but does not play an instrument
iii)Find the probability that member of the choir chosen at random does not play an instrument
iv)Find the probability that someone who does not play an instrument chosen at random, is in the choir.


(i) one fifth of pupils do neither leaving 320 pupils who do one or the other or both. this means that
220 play music only
70 sings only
30 do both

(ii) hence 70/400
(iii) there are 100 in the choir 70 of which do not play an intrument =>70/100
(iv) 150 pupils do not play an instrument 70 of which are in the choir => 70/150
Reply 2
[QUOTE="seekaye"]
Strange Dog
In a school of 400 pupils, 250 play a musical instrument and 100 sing in the choir.

The probability that a pupil chosen at random neither plays a musicla instrument nor sings in the choir is 1/5.

i)How many pupils both sing in the choir and play a musical instrument?
ii)Find the probability that a puipil chosen at random sings in the choir but does not play an instrument
iii)Find the probability that member of the choir chosen at random does not play an instrument
iv)Find the probability that someone who does not play an instrument chosen at random, is in the choir.


(i) one fifth of pupils do neither leaving 320 pupils who do one or the other or both. this means that
220 play music only
70 sings only
30 do both

(ii) hence 70/400
(iii) there are 100 in the choir 70 of which do not play an intrument =>70/100
(iv) 150 pupils do not play an instrument 70 of which are in the choir => 70/150


Thanks for the help man, but I still don't even get i) ... could you show me every calculation you used to work that one out please?
Reply 3
Wouldn't it be possible to do this with a Venn diagram? :confused:
Reply 4
Strange Dog
Thanks for the help man, but I still don't even get i) ... could you show me every calculation you used to work that one out please?



A venn diagram would help:

two overlapping circles one for M (plays Music) one for C (in choir)

A fifth of the 400 pupils is 80. So 80 goes outside both circles (ie in neither M nor C)

This leaves 320 pupils to assign in the circle
But you have 250 in M + 100 in C = 350 meaning 30 must be in both M and C
This means that you can put 30 in the overlap (intersection)
This leaves 220 in M but not C
Also 70 in C but not M

Once you have this diagram the rest of the question is straightforward

e.g. last part

Find prob someone who does not play an intsrument chosen at random is in the choir.

from diagram there are 150 people not playing an instrument (ie outside the M circle) 70 of which are in the choir => answer is 70/150
Reply 5
Thanks a lot; that really cleared things up. I have another irritating question now though, lol:

At a bank branch the manager has a staff of 12, consisting of 5 men and 7 women, including a Mr Brown and a Mrs Green. He has to make 4 staff of redundant, and he selects 4 staff at random.

i)How many different selections are possible? (12C4 = 495, right?)
ii)How many of these selections include botrh Mr Brown and Mrs Green?
iii)What is the probability that both Mr Brown and Mrs Green are made redundant

The manager then scraps this list and decides to make 2 men redundant and 2 women redundant instead.

iv) How many different selections are possible now? (5C2 x 7C2 i think)
v) Find the probability that both Mr Brown and Mrs Green are made redundant now

I'm stuck on ii), iii) and iv)... I hate stats!
Reply 6
At a bank branch the manager has a staff of 12, consisting of 5 men and 7
women, including a Mr Brown and a Mrs Green. He has to make 4 staff of redundant, and he selects 4 staff at random.

i)How many different selections are possible? (12C4 = 495, right?)

YES

ii)How many of these selections include botrh Mr Brown and Mrs Green?

NOW ONLY NEED TO CHOOSE 2 FROM 10 SO 10C2

iii)What is the probability that both Mr Brown and Mrs Green are made redundant

ANSWER (ii)/ANSWER (i)


The manager then scraps this list and decides to make 2 men redundant and 2 women redundant instead.

iv) How many different selections are possible now? (5C2 x 7C2 i think)
v) Find the probability that both Mr Brown and Mrs Green are made redundant now

IIF MR B AND MRS G ARE SACKED NEED 4C1 (POSSIBLE MEN) X C61 (POSSIBLE WOMEN)
=> 4C1 X 6C1 / [5C2 X 7C2]