Question

during summer vacation Tanuja wants to visit three cities, kolkata, bhubaneswar and chennai randomly. find the probability that she will visit (i) bhubaneswar before chennai (ii) bhubaneswar just before kolkata.

Answer 1

Answer on Question #60264 – Math – Statistics and Probability

Question

During summer vacation Tanuja wants to visit three cities, Kolkata, Bhubaneswar and Chennai randomly. Find the probability that she will visit

(i) Bhubaneswar before Chennai

(ii) Bhubaneswar just before Kolkata.

Solution

Let us denote the following events: B="Tanuja visits Bhubaneswar", C="Tanuja visits Chenai", K="Tanuja visits Kolkata". Then the space of all the possible outcomes has the next form:

$$\Omega = \{BCK, BKC, CBK, CKB, KBC, KCB\}, |\Omega| = 6.$$

(i) Let event $A =$ "Tanuja will visit Bhubaneswar before Chennai". It can be represented in the next form:

$$A = \{BCK, BKC, KBC\}, |A| = 3.$$

Then the required probability is equal to $\frac{|A|}{|\Omega|} = \frac{3}{6} = \frac{1}{2} = 0.5$.

(ii) Let event $D =$ "Tanuja will visit Bhubaneswar just before Kolkata". It can be represented in the next form:

$$D = \{BKC, CBK\}, |D| = 2.$$

Then the required probability is equal to $\frac{|D|}{|\Omega|} = \frac{2}{6} = \frac{1}{3}$.

Answer:

(i) $\frac{1}{2}$;

(ii) $\frac{1}{3}$.

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