Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is:Options25/3925/695/1331/65
Question
Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is:Options25/3925/695/1331/65
Solution
To solve this problem, we first need to calculate the total number of ways to select 2 persons out of 13, which is a combination problem. The formula for combination is C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
Step 1: Calculate total combinations The total number of ways to select 2 persons out of 13 is C(13, 2) = 13! / [(13-2)! * 2!] = 78.
Step 2: Calculate combinations without women The number of ways to select 2 persons out of 8 men is C(8, 2) = 8! / [(8-2)! * 2!] = 28.
Step 3: Calculate probability of selecting at least one woman The number of combinations that include at least one woman is the total combinations minus the combinations without women. So, it's 78 - 28 = 50.
Step 4: Calculate the probability The probability is the number of desired outcomes (combinations that include at least one woman) divided by the total number of outcomes (total combinations). So, the probability is 50 / 78 = 25 / 39.
So, the correct answer is 25/39.
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