ProbabilityHard
Question
A student has to match three historical events i.e. Dandi March, Quit India Movement and Mahatma Gandhi′s assasination with the years 1948, 1930 and 1942 and each event happens in different years . The student has no knowledge of the correct answers and decides to match the events and years randomly. Let Ei : (0 ≤ i ≤ 3) denote the event that the student gets exactly i correct answer, then
Options
A.P(Eo) + P(E3) = P(E1)
B.P(Eo) . P(E1) = P(E3)
C.P(E0 ∩ E1) = P(E2)
D.P(E0) + P(E1) + P(E3) = 1
Solution
P(Eo) = 
P(E1) =
P(E2) =
P(E3) =
So P(E0) + P(E3) = P(E1)
P(E0) . P(E1) = P(E3)
∵ E0 ∩ E1 = φ
So P(E0 ∩ E1) = 0
So P(E0 ∩ E1) = P(E2)
P(E1) =
P(E2) =
P(E3) =
So P(E0) + P(E3) = P(E1)
P(E0) . P(E1) = P(E3)
∵ E0 ∩ E1 = φ
So P(E0 ∩ E1) = 0
So P(E0 ∩ E1) = P(E2)
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