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in Statistics and probability by (52.5k points)

For i = 1, 2, 3, 4, let Ti denote the event that the students Si and Si+1 do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event T1 ∩ T2 ∩ T3 ∩ T4 is 

(A) 1/15

(B) 1/10

(C) 7/60

(D) 1/5

1 Answer

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Best answer

Answer is (C) 7/60

The probability of the event T1 ∩ T2 ∩ T3 ∩ T4 is

Now, the probability that at least one pair of students sit adjacent to each other is

The probability that at least two pairs of students sit adjacent to each other is

The probability that at least three pairs of students sit adjacent to each other is

The total arrangements is 

 5! = 5 × 4 × 3 × 2 × 1 = 120 

Therefore, the required probability is

(120 - 192 + 108 - 24 + 2)/120 = 14/120 = 7/60

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