Question

There are 5 students in a classroom, 3 from Group A and 2 from Group B. 3 apples were given to 3 out of the 5 students randomly. Calculate the probability that:
i) All 3 Group A students received the apples,
ii) At least 2 out of 3 Group A students received the apples.

Answer 1

what are you struggling with?

Answer 2

I don't know where to start

Answer 3

So let's try to think of the problem differently. Think of being given an apple as being CHOSEN to eat an apple. So then, we're choosing 3 people to eat apples :). So what's the probability that the first person chosen is from group A?

Answer 4

3/5

Answer 5

and the second person?

Answer 6

2/4

Answer 7

wait so its 3/5 times 2/4 times 1/3 = 1/10

Answer 8

yes :)

Answer 9

I'm stuck with part ii) though

Answer 10

mmhmm.... so are you familiar with permutations and combinations?

Answer 11

um no

Answer 12

so does at least 2 mean 2 or 3, or does it mean just 3?

Answer 13

2 or 3

Answer 14

Because we just did 3, we can just calculate the probability for 2 and add on to the probability for 3. How do we calculate the probability of two? Well, generally we'd use a formula (combinations), but let's not worry about it... here are the possibilities for choices where 2 are A
AAB
ABA
BAA
Did I miss any? how many are there?

Answer 15

3 combinations

Answer 16

Alright, so the interesting thing is that we can calculate the probability of AAB, ABA, and BAA separately, but you will actually find they turn out to be the same, because the denominator will be the same and only the order of the numbers will change.
Since any of these situations count as at least 2 apples being given to A, we need to calculate the probability of them all happening. In this case though, because they are the same, we can just do case AAB and then multiply that probability by 3. And what would case AAB be?

Answer 17

3/5 x 2/4 x 2/3 = 1/5

Answer 18

So what's the probability of 2 apples being given to group A? and using that, the probability of at least 2 apples being given to group A?

Answer 19

3/5, then add to 1/10 to get 7/10

Answer 20

yup!

Answer 21

Ah, I get it. Thank you :)

Answer 22

No problem :)