Probability

[punitkaur]

8. Out of a box that contains 4 black and 6 white mice, three are randomly chosen. What is the probability that all three will be black?

a) 8/125.
b) 1/30.
c) 2/5.
d) 1/720.
e) 3/10.

The way I did it is

no of ways 3 blacks can be chosen out of 4 is 4 C 3
Total ways = 10 C 3

answer = 4c3/10c3

another way to solve as the solution proposed -

The probability for the first one to be black is: 4/(4+6) = 2/5.
The probability for the second one to be black is: 3/(3+6) = 1/3.
The probability for the third one to be black is: 2/(2+6) = 1/4.
The probability for all three events is (2/5) x (1/3) x (1/4) = 1/30.

Are both the methods correct or just the second one.

In complex problems how to decide whether to choose the first or second?

Please help

[mp2437]

Both ways are correct as long as you are consistent.

[Brent@GMATPrepNow]

8. Out of a box that contains 4 black and 6 white mice, three are randomly chosen. What is the probability that all three will be black?

a) 8/125.
b) 1/30.
c) 2/5.
d) 1/720.
e) 3/10.

Here's the counting approach:

P(all 3 mice are black) = (# of ways to select 3 black mice)/(TOTAL # of ways to select ANY 3 mice)

# of ways to select 3 black mice
Since the order in which we select the mice does not matter, we can use COMBINATIONS
We can select 3 black mice from 4 black mice in 4C3 ways (= 4 ways)

TOTAL # of ways to select ANY 3 mice
We can select 3 mice from all 10 mice in 10C3 ways (= 120 ways)

ASIDE: If anyone is interested, we have a video on calculating combinations in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

So, P(all 3 mice are black) = 4/120
= 1/30
= B

Cheers,
Brent

[Brent@GMATPrepNow]

8. Out of a box that contains 4 black and 6 white mice, three are randomly chosen. What is the probability that all three will be black?

a) 8/125.
b) 1/30.
c) 2/5.
d) 1/720.
e) 3/10.

Another approach (using probability rules)

P(all 3 selected mice are black) = P(1st mouse is black AND 2nd mouse is black AND 3rd mouse is black)
= P(1st mouse is black) x P(2nd mouse is black) x P(3rd mouse is black)
= 4/10 x 3/9 x 2/8
= 1/30
= B

Cheers,
Brent