Koko (a cat) is trying to catch a mouse who lives under Susan’s house. The mouse
ID: 3301049 • Letter: K
Question
Koko (a cat) is trying to catch a mouse who lives under Susan’s house. The mouse has two exits, one outside and one inside, and randomly selects the outside exit 60% of the time. Each midnight, the mouse emerges for a constitutional. If Koko waits outside and the mouse chooses the outside exit, then Koko has a 20% chance of catching the mouse. If Koko waits inside, then there is a 30% chance that he will fall asleep. However, if he stays awake and the mouse chooses the inside exit, then Koko has a 40% chance of catching the mouse.
(a) Is Koko more likely to catch the mouse if he waits inside or outside? Why?
(b) If Koko decides to wait outside each midnight, then what is the probability that he will catch the mouse within a week (no more than 7 nights)?
Explanation / Answer
(a)
Probability of Koko being able to catch the mouse outside = Probability that mouse comes outside * Probability that koko can catch the mouse when it comes outside = 0.6*0.2 = 0.120
Probability of Koko being able to catch the mouse inside = Probability that mouse comes outside * Probability that koko is awake * Probability that koko can catch the mouse when it comes inside = 0.4*0.7*0.4 = 0.112
Thus Koko is more likely to catch the mouse outside
(b)
Probability that Koko catches the mouse on the very first day = 0.120
Probability that Koko catches the mouse on the second day = 0.88*0.12 =0.1056
Probability that Koko catches the mouse on the third day = 0.882*0.12 = 0.0929
Probability that Koko catches the mouse on the fourth day = 0.883*0.12 = 0.0817
Probability that Koko catches the mouse on the fifth day = 0.884*0.12 = 0.0719
Probability that Koko catches the mouse on the sixth day = 0.885*0.12 = 0.0633
Probability that Koko catches the mouse on the seventh day = 0.886*0.12 = 0.0557
So, probability that Koko catches the mouse within a week, waiting outside is:
0.120+0.1056+0.0929+0.0817+0.0719+0.0633+0.0557 = 0.5911
Hope this helps !
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