Question

There are 70 teachers in a school. Of the 38 male teachers, 8 teach Maths It is known that 2/7 of all teachers teach Maths. Find the probability that a teacher selected at random is.
(a) a male teacher or a teacher who teaches Maths.
(b) a female teacher or a teacher who teaches Maths.
(c) a female teacher or a teacher who does not teach Maths.

Answer 1

Draw a 2x2 grid with total. Fill in the blanks.

Answer 2

@ganeshie8

Answer 3

thanks for your help. However, the answer is 5/7 ..

Answer 4

@amistre64

Answer 5

@ajprincess

Answer 6

Your 2 x 2 grid looks good. Which question is still unanswered?

Answer 7

part a . haha. i cannot calculate the correct answer.

Answer 8

I think it is all but the square that is female non-maths, as the other squares are included in the requirements. Thus, 58/70?

Answer 9

the answer is 5/7

Answer 10

Which must come from 50/70. Or [8+12+30 ]/70

Answer 11

where comes 30?

Answer 12

Try this males = 8, non-maths males =30, but we have already counted 8 males in that, so those two are 8 + (30-8) = 30 and then 20 female non-maths gives 50 and the total denominator is 70.

Answer 13

but the question is asking "a male teacher or a teacher who teaches Maths"....

Answer 14

Yes, but we cannot double-count the males who do teach maths. I think I am right, but I am not sure.

Answer 15

However, i think 50 is non-maths teachers but not maths teachers....

Answer 16

i can ask my maths teacher tomorrow. let move onto part b first

Answer 17

Try: 1 minus all excluded. I think that is the easier way to see it and get 50/70.

Answer 18

this method is called complementary events, isn't it? So difficult..

Answer 19

Not sure of terminology. Yes, difficult.

Answer 20

and part b is similar to part a...

Answer 21

Yes. "OR" is the key. Means we cannot just multiply two independent probabilities as we can with "AND." OR means "either or both."

Answer 22

and part c ?
32/70+30/70=31/35?

Answer 23

i think the formula doesn't make sense..

Answer 24

ahh, i know how to do now!
for part a, "a male teacher or a teacher who teaches Maths" doesn't mean the male teacher teaches Maths!
Therefore,
a male teacher=38
a teacher who teaches Maths=12 (which is the number of female teachers as you said it cannot be double-count)

So, (38+12)/70=5/7

Answer 25

and for part b, a female teacher=32; a teacher who teaches Maths=8(which is the number of male teachers who teach Maths)

Therefore, 40/70=4/7

.......does it make sense?

Answer 26

"a male teacher or a teacher who teaches math" includes all males, and all those who teach math, except that we have already counted 8 of them as males.

Answer 27

all males means male teachers who teach non-Maths and Maths??

Answer 28

yes, all males means all of them regardless of what they teach.

Answer 29

oh i see. No wonder why i confused these questions.

And three parts i got the correct answer. Thanks for your help!!:)

do you know where does the permutation and combination concepts post in openstudy?

Answer 30

No, but I know that permutations consider order crucial, and the number of permutations of n things is n!.

Combinations ignore order, and the number of combinations of n things taken r at a time is n!/(r!)(n-r)!

These are the central concepts and equations.

Answer 31

does "ignore order" mean without repetition?

thank you so much! I must go to bed now as my time here is 11 pm already. Goodnight and million thanks:)

Answer 32

ignore order means the items are considered identical

Answer 33

I am in new York, here are you?

Answer 34

good night