The probability of a problem being solved by 3 students independently are 1 2 , 1 3 and α respectively. If the probability that the problem is solved is P S , then P S lies in the interval (where, α ∈ 0 , 1 )

Step-by-step solution

Let 3 students are A , B , C and their probability of solving problems is P A , P B , P C respectively. P A = 1 2 , P B = 1 3 , P C = α Probability of the problem is being solved, P S = 1 - P ( A C ∩ B C ∩ C C ) = 1 - P A C P B C P ( C C ) = 1 - 1 - P A 1 - P B 1 - P C = 1 - 1 2 2 3 1 - α = 2 3 + 1 3 α Hence, P S ∈ 2 3 , 1