mutually eclusive or independent event

A bag contains 7 red , 5 blue , 4 white and 4 blck balls . Find the probability that a ball drawn at random is red or white ?

Question :

I am confused at whether i call it a "mutual exclusive" or "independent events".

because for mutual exclusive events , we need to add up both the probability . and for independent events , we need to multiply.

What is this event ? mutually eclusive or independent event ..............please explain.

Thank you

total= 7 red +5 blue + 4 white + 4 black
total = 20 balls

success is choosing a red OR white [ when you say OR you add]
sucess = 11 balls
probability = 11/20 answer

prob = {C[1,7] + C [1,4] } / C[1,20] answer
C[a,b] means combination of b things taken a at a time

Arthur

Hello, defeated_soldier!

A bag contains 7 red, 5 blue, 4 white, and 4 black balls.
Find the probability that a ball drawn at random is red or white.

I am confused at whether i call it a "mutual exclusive" or "independent events".
because for mutual exclusive events, we add the probabilities,
and for independent events, we multiply.

What is this event? ... mutually exclusive or independent event?

Click to expand...

Try to un-confuse yourself . . . keep the situations separated.


We are concerned with "mutually exclusive" if it is an OR problem.
. . That is when we try to add probabilities.

In this problem, we want: \(\displaystyle \,P(R\,or\,W)\)

We see that: \(\displaystyle \,P(R)\,=\,\frac{7}{20}\,\) and \(\displaystyle \,P(W)\,=\,\frac{4}{20}\)

IF the events are mutually exclusive, we can just add the probabilities.
Can the two events happen at the same time?
. . No, we cannot draw a Red ball and a White ball at the same time.
. . The events are mutually exclusive.
Therefore: \(\displaystyle \(R\,or\,W)\:=\:\frac{7}{20}\,+\,\frac{4}{20}\:=\:\frac{11}{20}\)


We are concerned with "independent events" if it is an AND problem.
. . That is when we try to multiply probabilities.

This problem is not an "and" problem.
. . An "and" means that two events will occur.

An example might be:
. . Two balls are drawn in succession.
. . What is the probability that both are red?

We want: \(\displaystyle \,P(1^{st}\text{ is Red }and\:2^{nd}\text{ is Red})\)

We know that: \(\displaystyle \,P(1^{st}\text{ is Red}) \,=\,\frac{7}{20}\)
. . But \(\displaystyle P(2^{nd}\text{ is Red})\) depends on whether the first was Red or not.

If the first ball is replaced before the second ball is drawn,
. . the events are independent.
With both draws, there are 7 Reds among the 20 balls:
. . \(\displaystyle \,P(Red) \,=\,\frac{7}{20}\) each time.


Hope this helps . . .

excellent explanation . I love it .

Thanks soro for such a detailed and excellent explanation . it helped me highly.
Thanks arthur for the tips .

Thank you very much

defeated_soldier

Hi ,

sorobon

could you please tell which software you are using for mathematical notations ?

can you copy-paste the notation directly from the clipboard to this forum html ?

It's not software. Just type out the code. Click on quote at the upper right corner of his post to see.