Guide 4 p 93 #8
In a diving competition each diver has a 20% chance of a perfect dive.The first perfect dive of the competition,but no subsequent dives will recieve a perfect score.If Janet is the third diver to dive,what are her chances of recieving a perfect score?

A pretty straight forward solution is .8 x .8 .2 =.128 x 100= 12.8%

I wached a session of 'Thursdays with Ron' and it appeared a similar question was asked-

On his drive to work, Leo listens to one of three radio stations, A, B, or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns to B. If B is playing a song he likes, he listens to it; if not, he turns to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is .30 that at a any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?

A .027
b .090
c .417
D .657
e. .900

the solution to this was 3/10 + (7/10 * 3/10) + (7/10 * 7/10 * 3/10)

my question is why can you not use this same theory on the initial question and go: 1/5 + (4/5 *1/5) + 1/5 and get the answer you are looking for?

Let me try to help you yo understand difference between these two questions. first I will explain question in studay hall.

if you rephrase the question when does Leo listens to the song he likes?

1. Leo turns to A, listens a song and he likes the song
OR
2. Leo turns to A, listens a song, he does not like it and turns to B and he likes the song
OR
3. Leo turns to A, listens a songand he does not like it; turns to B and he does not like the song; turns to C and likes the song
so you calucalte probabalitiy for each scenario and add them as Ron explained in study hall

Rephrase the strategy guide question.
there are 3 divers and what is the probability of 3rd diver get perfect score. To this can happen only when 2 divers before him should not get perfect score and he gets perfect scope. if you compare with other question, this scenario is equivalent to 3rd scenario of other question.

I hope this helps you

thanks for the explanation. Steven, please let us know if you need any further help with this one..

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Tim Sanders
Manhattan GMAT Instructor

Just adding another approach to music question. Of the three stations, we are looking for at least one station to provide him good music. Consider cases GBG, GGG, BBB, ..... If we know the probability of scenario not providing any good music, then 1-that probability will be the answer for probability of providing good music by any one station. So probability of BBB is 7/10*7/10*7/10 . Probability of getting good music is 1 - (343/1000) = 0.657.

Agreed, thanks for your input.

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Jamie Nelson
ManhattanGMAT Instructor

There is a typo here: 7 * 7 * 7 = 343, not 434.

Thanks, you are right! Fixed above.

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Jamie Nelson
ManhattanGMAT Instructor