Analysis and Approaches for IBDP Maths Ebook 1 | Page 279

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3. Lydia notices that on windy days, the probability she catches a fish is 0.13 while on nonwindy
days the probability she catches a fish is 0.59. The probability that it will be windy
on a particular day is 0.45.
(a)
(b)
(c)
(d)
On a randomly selected day, find the probability that Lydia catches a fish.
[4]
Given that Lydia catches a fish on a particular day, find the probability that it was
not windy.
[3]
In a week of seven days, find the probability that Lydia catches a fish on exactly
three days.
[2]
After n days, the probability that Lydia catches a fish on at least two days is
greater than 0.93. Find the least value of n .
[5]
4. In an experiment, a mouse is placed in a maze. There are two doors, A and B, and the
mouse has to choose one of them to escape from the maze. Both doors are linked to
various paths. Some paths in the maze lead to a trap and others to escape doors. The
probability that the mouse chooses door A is p . If it chooses the door A, then the
probability that it reaches a trap is 0.7. If it chooses the door B, then the probability that it
reaches a trap is 0.52.
(a) Find the probability that the mouse reaches an escape door, giving the answer in
terms of p .
[4]
(b) Given that the mouse reaches an escape door, find the probability that it chooses
the door A, giving the answer in terms of p .
[3]
Assume that p � 0.61.
20
(c)
(d)
If the experiment is repeated for eight times, find the probability that the mouse
reaches an escape door on exactly six times.
After n experiments, the probability that the mouse reaches an escape door on
more than two trials is greater than 0.99. Find the least value of n .
[2]
[5]
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