Question 862166: 2. A candidate is selected for interview for 3 posts. For the first post, there are 3 candidates, for the second, 4 and for the third post there are 2 candidates. What is the probability that the candidate is selected for at least one post?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are 3 candidates for job 1 and 4 candidates for job 2 and 2 candidates for job 3.
we can look at the total possible combinations for all 3 jobs.
those possible combinations would be 3 * 4 * 2 = 24.
we can call the candidates for job 1: candidate 1a, 1b, 1c.
we can call the candidates for job 2: candidate 2a, 2b, 2c, 2d.
we can call the candidates for job 3: candidate 3a, 3b.
our candidate is candidate "a" for all 3 jobs.
there are 24 possible combinations for the 3 jobs.
they are:
1a 2a 3a ***** 1
1a 2a 3b ***** 2
1a 2b 3a ***** 3
1a 2b 3b ***** 4
1a 2c 3a ***** 5
1a 2c 3b ***** 6
1a 2d 3a ***** 7
1a 2d 3b ***** 8
1b 2a 3a ***** 9
1b 2a 3b ***** 10
1b 2b 3a ***** 11
1b 2b 3b
1b 2c 3a ***** 12
1b 2c 3b
1b 2d 3a ***** 13
1b 2d 3b
1c 2a 3a ***** 14
1c 2a 3b ***** 15
1c 2b 3a ***** 16
1c 2b 3b
1c 2c 3a ***** 17
1c 2c 3b
1c 2d 3a ***** 18
1c 2d 3b
if you look for all occurrences where "a" is entered at least once (could be 1a, 2a or 3a), then you will find the there are 18 out of the 24 possible combinations where "a" is counted at least once.
this gives you a probability of 18/24.
the formula for this type of problem is:
p(a or b or c) = p(a) + p(b) + p(c) = p(ab) - p(ac) - p(bc) + p(abc).
p(a) is equal to 1/3.
p(b) is equal to 1/4.
p(c) is equal to 1/2.
p(ab) means the probability of a and b occurring at the same time, which is equal to p(a) * p(b).
the same meanings apply for p(ac) and p(bc).
the formula becomes:
p(a or b or c) equals:
p(a) + p(b) + p(c) = p(ab) - p(ac) - p(bc) + p(abc).
replace the letters with their values and you get:
p(a or b or c) equals:
1/3 + 1/4 + 1/2 - (1/3)(1/4) - (1/3)(1/2) - (1/4)(1/2) + (1/3)(1/4)(1/2)
this becomes:
8/24 + 6/24 + 12/24 - 1/12 - 1/6 - 1/8 + 1/24
this becomes:
26/24 - 2/24 - 4/24 - 3/24 + 1/24
this becomes:
26/24 - 9/24 + 1/24
this becomes:
27/24 - 9/24
this becomes:
18/24 *****
the formula gives us the same answer we derived by looking at each possible combination.
this is to be expected since this formula was derived to take care of this particular situation.
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