A student selects 5 distinct days from the month of April ( 30 days) to take mock tests. The selected days are arranged in chronological order. Given that the 3^ rd mock test is scheduled on April 15^ th , the conditional probability that the 2^ nd mock test is on April 10^ th and the 4^ th mock test is on April 22^ nd is

Step-by-step solution

Let the selected days be d₁ Let A be the event that the 3^ rd mock test is on April 15^ th ( d₃ = 15 ). For event A to occur, d₁ and d₂ must be selected from the days 1 to 14 , which can be done in ¹⁴C₂ ways. d₄ and d₅ must be selected from the days 16 to 30 (a total of 15 days), which can be done in ¹⁵C₂ ways. Total number of outcomes in event A , n(A) = ¹⁴C₂ ¹⁵C₂ = 91 105 = 9555 . Let B be the event that d₂ = 10 and d₄ = 22 . We need to find P(B|A) = n(A B) n(A) . For the intersection A B , we have d₂ = 10 , d₃ =