Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is alteast one graduate among them ?a)1/6b)5/8c)3/8d)5/6Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Problem:
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?

Solution:
To solve this problem, we can use the concept of complement probability. The complement of the event 'at least one graduate among the selected three' is the event 'no graduates among the selected three.'

Step 1: Determine the total number of ways to select 3 persons from a group of 10.
The total number of ways to select 3 persons from a group of 10 is given by the combination formula:
C(10, 3) = (10!)/(3!(10-3)!) = 120.

Step 2: Determine the number of ways to select 3 non-graduates from a group of 6 non-graduates.
The number of ways to select 3 non-graduates from a group of 6 non-graduates is given by the combination formula:
C(6, 3) = (6!)/(3!(6-3)!) = 20.

Step 3: Calculate the probability of selecting 3 non-graduates.
The probability of selecting 3 non-graduates is given by the number of ways to select 3 non-graduates divided by the total number of ways to select 3 persons.
P(no graduates) = 20/120 = 1/6.

Step 4: Calculate the probability of at least one graduate.
The probability of at least one graduate is equal to 1 minus the probability of no graduates.
P(at least one graduate) = 1 - P(no graduates) = 1 - 1/6 = 5/6.

Therefore, the probability that there is at least one graduate among the three selected persons is 5/6, which corresponds to option D.

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