10 t-shirts are available to choose. 5 of them are printed,

Question

10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.

Please explain the steps (procedure)

Anonymous · Answer

If the answer is 5/24, i will explain.

GoalStanford · Answer

P(all non-printed) = 5C3/10C3=5*4*3/10*9*8=1/12
P(atleast one printed)=1-1/12=11/12

carsen · Answer

Pardon me GUEST ...

I can let know the answer only if you explain. Sorry about that.

Goal Stanford... 

I understand the first step - Desired/Total combinations.

But

  P(atleast one printed)=1-1/12=11/12   - Can you explain me this step?.

Thanks bro.

Emmanuel · Answer

1. Probability of at least 1 being a printed = 1 - P(none of them is printed).

2. P(all 3 are plain) = 5/10*4/9*3/8 = 1/12!

3. The answer is 1 - 1/12 = 11/12.

nina911 · Answer

do you mean how many methods or anything other?

Nina from forest and lakes

KarishmaB · Answer

You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.

You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2 = 10 ways.

So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.

So probability of picking at least one printed t-shirt = 110/120 = 11/12

BrentGMATPrepNow · Answer

When it comes to probability questions involving "at least," it's best to try using the complement, as the above solutions have done. 
However, what if you didn't spot that shortcut? 
No problem, it will just take us a little bit longer.

P(at least 1 printed shirt) = ( # of outcomes with at least 1 printed shirt )/( TOTAL # of possible outcomes )

Always start with the denominator.

TOTAL # of possible outcomes  
We have 10 shirts and we must select 3. 
Since the order in which we select the shirts doesn't matter, we can use combinations. 
We can select 3 shirts from 10 shirt in 10C3 ways (=  120  outcomes)

# of outcomes with at least 1 printed shirt  
We have 3 cases: 
 Case 1 : 1 printed shirt and 2 plain. So, select 1 of the 5 printed, and select 2 of the 5 plain.
# of outcomes = (5C1)(5C2) = (5)(10) = 50
 Case 2 : 2 printed shirts and 1 plain. So, select 2 of the 5 printed, and select 1 of the 5 plain.
# of outcomes = (5C2)(5C1) = (10)(5) = 50
 Case 3 : 3 printed shirts and 0 plain. So, select 3 of the 5 printed, and select 0 of the 5 plain.
# of outcomes = (5C3)(5C0) = (10)(1) = 10

Total number of outcomes = 50 + 50 + 10 =  110

So, P(at least 1 printed shirt) =   110  /  120  
= 11/12

Cheers,
Brent

AkshdeepS · Answer

Karishma,

This is the combinatorics approach if I am not wrong. Can you tell me how to solve this with probability approach.

BrentGMATPrepNow · Answer

Emmanuel posted a nice probability approach above.

Cheers,
Brent

AkshdeepS · Answer

Thanks a lot Brent.

aekukula · Answer

Hi There,

Allow me to give u all the approach i did with this question

Firstly, there are 10 Shirts, which is 5 Printed (Pr) and 5 Plain (Pl)

and we need to find the probability for  at least  one of them 3 shirts is Printed (Pr)

and this can be done with the following event :

1 of 3 shirts is Pr (Pr Pl Pl) : there are 5C1 combination of this event 
or
2 of 3 shirts is Pr (Pr Pr Pl) : there are 5C2 combination of this event
or
all of the shirts is Pr (Pr Pr Pr) : there are 5C3 combination of this event

(please note that order does not matter so we can use Combination in here)
(also notice the "or" above so that means we must use + (plus) for the total event)

and for the total probability of all shirts, there is total 3 shirts out of 10 we can use 10C3

So in the end we can calculate the probability with the following equation : (5C1 + 5C2 + 5C3) / 10C3 = 5/24

there you have it !

bethebest · Answer

Do we not need to consider the sequence in this - how do we decide?

KarishmaB · Answer

No. Here you are just "selecting" 3 t-shirts. If you had to decide the sequence in which you could wear them over 3 days, then you would need to arrange them too. In this post, I have tried to explain the difference: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/01 ... mbination/

psahoo · Answer

P(all non printed)= 5C3/10C3 = 10/120 = 1/12
P(atleast one printed) = 1-1/12 = 11/12

HKD1710 · Answer

probability of At least one is probability of (1 - none)

there are 5 non painted t-shirts that comes in 'none' category. choose 3 out of these 5.

Probability of at least one of them is a printed t-shirt = 1 - (5choose3/10choose3) = 1 - 1/12 = 11/12.

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10 t-shirts are available to choose. 5 of them are printed,

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