What is the chance that he received $60 ?

Question

Eric received 3 red packets. Each red packet had an equal chance of having either a $5, $20, or $50 note.
What is the chance that he received $60 ?

a. 2/33
b. 4/27
c. 1/9
d. 1/6

Answer 1

I'm not a 100% sure if my answer is correct, but I'm going to give it a try anyways.

 

You have 3 envelopes and each envelope has an equal chance of being 5, 20, and 50. That means, for example, drawing one 5 will not affect the probability of drawing another 5. If this is the case, the total number of possible outcomes are as follows:

3 x 3 x 3 = 27

 

Now, you want to assemble all the combinations of 5, 20, 50 that would sum up to 60. I got the following combinations:

5, 5, 50

5, 50, 5

50, 5, 5

20, 20, 20

 

There you have 4 combinations out of the 27 total outcomes. That's why you should have a probability 4/27 of obtaining a total of 60 dollars. Hope this helps.

Answer 2

There are three envelopes which each have independent choices between three options.  Thus, there are a total of 3*3*3=27 different ways the money can be configured.

 

Of those 27 ways, four of them add up to exactly $60:

 

1.  $5+$5+$50

2.  $5+$50+$5

3.  $50+$5+$5

4.  $20+$20+$20

 

Since there are 27 equally likely ways for Eric to receive money in this manner, and in four of those ways he receives exactly $60, he has a 4/27 chance of receiving $60.