Question hi surry, a class consists of 8 boys and 6 girls, a committee of three persons is to be constituted fromthe class,find the prb that the committee consists of (a)3 boys
(b)1 girl and 2 boys.
(2) a and b are two events defined in a simple space with p(a)=0.5 and p(b) = k, and the prb of at least a or b occuring is 0.80,obtain the value of k such that
(a) a and b are independent
(b) a and b are mutually exclusive.
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Answer 1. a class consists of 8 boys and 6 girls, a committee of three persons is to be constituted from the class,find the prb that the committee consists of 3 boys
So, we need to pick 3 boys from the 8.
We can pick the first in 8 ways ( any one of the 8 persons in OK).
We can pick the second in 7 ways, ( as one has been picked already).
we can pick the third person in 6 ways ( as two have been selected).
So, total number of ways is 8 * 7 * 6.
But wait, you may have ways like this
Select A, then B, then C
But also, A, then C, then B
or, B, A, C
or, B, C, A
or, C, A, B
or, C, B, A
these are different ways (permutations) but they are the same group, right?
i.e for each group, we are counting them 3*2 = 6 times.
So, the actual number of combinations is
8*7*6/ 3*2*1
( This method works for all scenarios of selecting X things out of Y
i.e you can select 2 things out of 7 in 7*6/2*1 ways,
you can select 4 things out of 9 in 9*8*7*6/4*3*2*1 ways
Try these out step by step as above, and see if you get these
If you don't write to me at surajit@gmail.com)
2. Now solve this question yourself:
a class consists of 7 boys and 9 girls, a committee of three persons is to be constituted from the class,find the prb that the committee consists of 3 girls.
Got it?
send me the answer.
3. Now lets try this:
a class consists of 8 boys and 6 girls, a committee of three persons is to be constituted from the class,find the prb that the committee consists of 1 girl and 2 boys.
What does this mean?
You have to pick 1 girl from 6 girls, and
you have to pick 2 boys from 8 boys.
In how many ways can you pick 1 girl from 6 girls?
