Probability question-Ron Purewal's video

[dddanny2006]

Hey there

Im finding it difficult to digest the methodology used in this problem.

Source-Ron Purewal video

Official answer-D

On his drive to work,Leo listens to one of the 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;it not,he turns off the radio.For each station,the probability is 0.30 that at any given moment the station is playing a song he likes.On his drive to work,what is the probability that Leo will hear a song he likes?

a. 0.027
b. 0.090
c. 0.417
d. 0.657
e. 0.900


My doubt is --

1)When we solve to find the probability that Leo will hear a song he likes--Why cant 0.30*0.30*0.30 or 0.30+.30+.30 be the answer?

Please differentiate between the two.

Also,the following is the right way to solve this problem--

Method 1
Prob(Leo likes first station) +Prob(Leo doesnt like first station,but like second one)+Prob(Leo doesnt like first,second,but like the third)
=P1 + P2 +P3
=(0.30) + (0.30*0.70) + (0.30*0.30*0.70) = 0.657

There's another way to do this problem its
Method 2
P(No station playing the song)=1-(0.7*0.7*0.7)=0.657

2)What I dont understand is we directly multiply .7*.7*.7 in the second method,but when we solve using the first method we have the extra terms like 'not' and 'will' causing p2 to have 0.3 and 0.7,while p3 has 0.3 0.3 and 0.7

Please answer doubt 1 and doubt 2 thats in bold.Also the difference between method 1 and method 2.Im not finding probability easy at all,is there a way to master it?


Thanks Ron

[RonPurewal]

Remember the two basics of probability. (Both also apply to combinatorics):

1/
If you want to find the probability of something AND something else, then multiply the individual probabilities.

2/
If you want to find the probability of something OR something else, then add the individual probabilities.
Note -- there must be no overlap between the two situations for this to work.

1)When we solve to find the probability that Leo will hear a song he likes--Why cant 0.30*0.30*0.30 or 0.30+.30+.30 be the answer?

Read the given situation carefully. If Leo hears a song he likes, he won't change the station.
If you do 0.30 * 0.30 * 0.30, then that's the chance that all three stations are playing a song that Leo likes. But that's not a situation that Leo would ever be exposed to, because, if he liked the song on the first station, he wouldn't switch to the others.

You can't add the probabilities, because the situations overlap with each other. I.e., it's perfectly well possible that there could be a good song on more than one of the stations.

[RonPurewal]

2)What I dont understand is we directly multiply .7*.7*.7 in the second method,but when we solve using the first method we have the extra terms like 'not' and 'will' causing p2 to have 0.3 and 0.7,while p3 has 0.3 0.3 and 0.7

This is more of the basics above.

If Leo doesn't like what's playing, he will go through all the stations. So, the chance that he hears nothing he likes is "bad song on #1 AND bad song on #2 AND bad song on #3". So, you multiply the probabilities.

As for the other stuff -- try applying the basics above. Think about what each situation represents. (For instance, if there's a bad song on station #1 but a good one on station #2, then Leo will only encounter those two stations, and not #3.)