The following question has two statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. Two numbers have been selected from sets A & B. find the probability of numbers selected being co - primes. I. Set A = (2, 3, 4) II. Set B = (5, 6, 7, 8)?

Option 4 : Statement I and statement II together are sufficient to answer the question.

Let’s check each statement individually -

Statement I -

Set A = (2, 3, 4)

As we can’t find the reference about numbers belonging to set B ∴ statement Ii is not sufficient to find the probability of selecting co-prime numbers.

Statement II -

Set B = (5, 6, 7, 8)

As we can’t find the reference about numbers belonging to set A ∴ statement II is not sufficient to find the probability of selecting co-prime numbers.

When both statements are considered -

Favorable co-prime sets are – (2, 3), (2, 5), (2, 7), (3, 4), (3, 5), (3, 7), (3, 8), (4, 5), (4, 7)

And total numbers of sets of selecting 2 numbers at a time = number of numbers in set A × number of numbers in set B

∴ Total numbers of sets of selecting 2 numbers at a time = 3 × 4

∴ Total numbers of sets of selecting 2 numbers at a time = 12

Probability of selecting co-prime numbers = Favorable number of co-prime sets/ Total number of sets = 9/12 = 3/4

∴ Both statements are required to find a solution.