jlgdr wrote:
ctrlaltdel wrote:
Mike recently won a contest in which he will have the opportunity to shoot free throws in order to win $10,000. In order to win the money Mike can either shoot 1 free throw and make it, or shoot 3 free throws and make at least 2 of them. Mike occasionally makes shots and occasionally misses shots. He knows that his probability of making a single free throw is p, and that this probability doesn't change. Would Mike have a better chance of winning if he chose to attempt 3 free throws?
(1) p < 0.7
(2) p > 0.6
I didn't quite get this one
This is my procedure
OK if he shot one time only probability will be 'p'
If he makes at least two shots then probability will be: Probability of making all three shots + Probability of making 2 shots and missing 1 shot
Let's see probability of making all three is p^3
Probability of making 2 out of 3 is 3C2 * p^2* (1-p)
So question goes down to is p> 3(p^2)(1-p) + p^3?
Is 2p^2 - 3p + 1 <0?
Statement 1
If we replace 0.7 for p we get that yes, it is always negative hence true
Sufficient
Statement 2
Clearly insufficient.
Could someone explain if I'm wrong somewhere? I'm mainly concerned about the formulation of the question rather than in the solving part but still could have made an error
Many thanks
Cheers
J
First of all, my friend, I think you have made a mistake in opening the brackets. I got it as 3p^2- 2p^3 -p < 0 (I'm bad at algebra )
Secondly, Why to complicate this question? By reading it you can understand it will involve cubes and squares + fractions. So its rather better to put your own values (under the permissible limit). My friend, solve question strategically and not mathematically
Third, this may not sound the best way to solve but you can do a little thinking before diving in with values.
A probability of < 0.7 can mean it could 0.1 or 0.6
if its 0.1 ----> if you are very lucky you might get a throw in once chance but 2 out 3 throws could mean tough for you.
if its 0.6 ----> More than half of the time you get a shot. You might or might not get it in one chance but you are better off with taking three shots as you are aware half of the times you get the shot
INSUFFICIENT
p > 0.6
Obviously here you can easily say, your probability is quite good. Although you don't get every shot (p=1, read question he occasionally misses the shot so p =1 is not possible ) but you mostly get the shot so you better go for three shots than one.
It didn't take me much time to think this obviously reading/writing this might seems like a long process but it seriously doesn't even take more than half a minute. After this, you can assume some value to confirm
SUFFICIENT
Note that had they not written "occasionally he misses the shot" it would have been tough as p> 0.6 could mean p=1
So if you always get a shot than taking one or three doesn't matter.