Kashvi, Kalyani and Sara of class 12 are given a problem in Accounts whose respective probabilities of solving are 2/5, 1/4 and 1/6. They were asked to solve it independently. The probability that the problem is solved is:

The correct answer is Option 3: 5/8.

We are given the individual probabilities of solving the problem:

P(Kashvi solves) = $\frac{2}{5}$,   P(Kalyani solves) = $\frac{1}{4}$,   P(Sara solves) = $\frac{1}{6}$

Since they solve the problem independently, the key insight is to use the complement rule:

P(problem is solved) = 1 - P(none of them solves it)

Step 1: Find the probability that each person does NOT solve the problem.

P(Kashvi does NOT solve) = $1-\frac{2}{5}=\frac{3}{5}$

P(Kalyani does NOT solve) = $1-\frac{1}{4}=\frac{3}{4}$

P(Sara does NOT solve) = $1-\frac{1}{6}=\frac{5}{6}$

Step 2: Find the probability that NONE of them solves the problem.

Since they work independently, we multiply their individual probabilities of failure:

$P\left(\text{none solves}\right)=\frac{3}{5}\times \frac{3}{4}\times \frac{5}{6}$

$=\frac{3\times 3\times 5}{5\times 4\times 6}=\frac{45}{120}=\frac{3}{8}$

Step 3: Apply the complement rule to find the probability that the problem IS solved.

$P\left(\text{problem is solved}\right)=1-P\left(\text{none solves}\right)=1-\frac{3}{8}=\frac{5}{8}$

Therefore, the probability that the problem is solved is 5/8.