A rat is placed into the set of rooms shown in the figure below. When the rat he

Question

A rat is placed into the set of rooms shown in the figure below. When the rat hears a bell it moves to the other room, or not, depending on how playful its feeling. The probability that the rat will move to room B given that it is in room A is 1/3. The probability that the rat will move to room A given that it is in room B is 1/2.

The rat is initially placed into room B.

(a) What is the probability that the rat is in room B after the bell has rung twice?

(b) If the rat is observed to be in room B after two bells what is the probability that the rat was in room B after one bell?

Explanation / Answer

a)P(rat in room B after bell rung twice)=P(in first ring moves to room A and then comes back in room B on second ring)+P(in first ring remains in room B and in second ring remains in room B)

=(1/2)*(1/3)+(1/2)*(1/2)=1/6+1/4 =10/24 =5/12

b)

P(rat was in room B after 1 bell|rat is in room B after 2 bells)

=P(in first ring remains in room B and in second ring remains in room B)/P(in room B after 2 bells)

=(1/2)*(1/2)/(5/12)=3/5

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.