WT Pg 94 Qn 13

[s1800028]

In the town of Z, the lion roars on some days and not on others. If a day is chosen at random from last March, what is the probablity that on that day, either the town lion roared or it rained?

I choosed C because (1) says that the lion never roars on both days and from (2), I can find out how many days the lion roared and how many days it rained.

ie x - roar days
y - rain days

x + y = 30
x = y - 10

--> y - 10 + y = 30
--> y = 20, x = 10

hence I can find the probablity. Why is C wrong?

[nehag84]

Pls post the original question...

[Ben Ku]

For convenience, here is the original question:
In the town of Z, the lion roars on some days and not on others. If a day is chosen at random from last March, what is the probability that on that day, either the town lion roared or it rained?
(1) Last March, the lion never roared on a rainy day.
(2) Last March, the lion roared on 10 fewer days than it rained.

The question asks for the P(roar OR rain). This means P(roar) + P(rain) - P(roar AND rain).

Statement (1) says that P(roar AND rain) = 0. But we still don't know anything about P(roar) or P(rain). So (1) is insufficient.

Statement (2) says that Roar = Rain - 10. However, we still don't know how many days it rained or the lion roared. So (2) is insufficient.

Combining the statements, we cannot determine P(Rain) OR P(roar), so the answer must be (E).

Your error is x + y = 30 (I think you meant 31), because you are assuming that on EVERY day in March, EITHER the lion roared OR it rained, however there might be days when neither happened.

[s1800028]

Hi Ben,

But the answer in page 97 says "30 (the number of days in March)".
Hence I am assuming 30 days for March.

[chanelzr]

where lies my mistake?

Firstly, I use "x" to represent the days the lion roars, then "31-x" are the days the lion doesn't roar;

Secondly, I use "y" to represent the rainy days, then "31-y" shall be the non-rainy days.

Condition (2) can thus be interpreted as:

x (days the lion roars) = 31-y (rainy days) -10
x + y = 21

Condition (1) tells us that P(x and y) = 0
"x + y" can be deduced as "either the lion roared or it rained"

Therefore, the probability should be 21/31.

[chanelzr]

I found my error: "31-y" are "non-rainy" days
...
how careless I am:(

[Ben Ku]

Hope everything's cleared up!