JEE Main · 2005 · 08 May 2005 · Offline · Probability

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Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

(A) $\frac{2}{9}$
(B) $\frac{1}{9}$ ✓ Correct
(C) $\frac{8}{9}$
(D) $\frac{7}{9}$

Answer: (B)

Solution

Each person chooses independently among the

3

houses, giving

3^{3} = 27

equally likely outcomes. All three choosing the same house can happen in

3

ways, one for each house, so the probability is

\frac{3}{27} = \frac{1}{9}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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