Probability (right handed and plays cello)?

[paragon]

Hello,
The question I am currently having trouble with is finding the answer to the problem as follows:
A string orchestra has ten members who plays violin, three who play viola,five who play cello and two who play double bass. There are fourteen members who are right-handed. If a member of this string orchestra is chosen at random, what is the probability that he or she is:
Right handed and plays the cello?

I have figured out the total people is 20 and that P(right handed)= 14/20 and P(cello players)= 5/20
What I have done, is minus the 14/20 from 5/20 to get a probability of 9/20 is that correct?
or would someone please show me the correct way of doing it.
Thanks.

 

[tkhunny]

What I have done, is minus the

Please never say that again.

What I have done, is [subtract] the 14/20 from 5/20 to get a probability of 9/20 is that correct?

Of course, you mean 14/20 - 5/20, not what you have stated. Communication is very important. Please work on it.
You should have had a discussion about "Independent Events". Have you had this introduction?
Somewhere in there, you should have encountered this idea, P(A and B) = P(A)*P(B). There is no subtraction in there. Give it another go.

 

[paragon]

Got it....
P(RIght handed and cello)= P(14/20)*P(5/20)= P(70/400) and if simplified to its simplest form it would be P(7/40).
Yea, I have had the "independent Events" talk at some point, however it was long ago and so it's just a matter of me forgetting.
I will definitely imprint the arithmetic language into my brain and check for minor errors next time.
Anyways, thanks for the assistance.

 

[tkhunny]

Got it....
P(RIght handed and cello)= P(14/20)*P(5/20)= P(70/400) and if simplified to its simplest form it would be P(7/40).
Yea, I have had the "independent Events" talk at some point, however it was long ago and so it's just a matter of me forgetting.
I will definitely imprint the arithmetic language into my brain and check for minor errors next time.
Anyways, thanks for the assistance.

Let's fix the notation problem while we're at it. The "P()" seems to have gotten out of control.

P(RIght handed and cello)= P(Right handed)*P(cello) = (14/20)*(5/20)= (70/400) = 7/40

Good work.