Multiple choice

Passage

Directions: Study the given information carefully and answer the following question. 3 groups A, B and C from a school went for a picnic. In each group, there were boys, girls and teachers. In group A, number of boys is 3 more than that of girls. If we have to select one member from this group, then the probability of him being a teacher is 4/11. In group B, number of girls is 50% more than that of boys. If 2 persons are selected from group B at random, then probability of both being teachers is 1/136. Total number of persons in group B is 17. In group C, the ratio of teachers to boys is 1 : 3 and that of teachers to girls is 1 : 4. Total number of persons in this group is 48.

If two persons are selected at random from all groups, then what are the chances of either both being teachers or both being girls?

  1. 661/2850

  2. 47/76

  3. 75/76

  4. 571/2850

  5. 47/5700
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A Correct answer
AI explanation

The total number of teachers across all groups is 4 from group A, 2 from group B, and 4 from group C, giving 10 teachers. The total number of girls across all groups is 7 from group A, 6 from group B, and 16 from group C, giving 29 girls. Using the combinations formula for selecting 2 people from all groups out of 81 total people, the probability of picking either 2 teachers or 2 girls is (10C2 plus 29C2) divided by 81C2. This evaluates to (45 plus 406) divided by 3240, which simplifies to 661/2850.

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