Probability Question

Question

If a die is rolled 4 times, what is the probability that the outcome will be 2 at least 3 times?

achiever01 · Answer

(1*1*1*5C1)*4+(1*1*1*1)*4 
--------------------------- 
 6^4

= 1/54.

whats OA?

gurpreetsingh · Answer

IMO

(1*1*1*5C1)*4+(1*1*1*1)*1 = 21/6*6*6*6 = 7/2*216 = 7/432
---------------------------
6^4

achiever01 · Answer

Hi Gurpreet,

I got the same answer as yours earlier.. however later i multiplied 4 in the second case. see  red

(1*1*1*5C1)*4+(1*1*1*1)*  4   
---------------------------
6^4
 
Why there wont be 4 cases in the second situation(all four 2's) ??
Is it because the four cases in this situation are not different??

aiming4mba · Answer

The OA is 7/432. Gurpreet, could you please explain your method? Thanks.

gurpreetsingh · Answer

Atleast three means : case1( prob of 3 times) + case 2( prob of 4 times)

for P(of 2 for 3 times ) =( 1/6 * 1/6 * 1/6 * 5/6 )* 4
here 1/6 is the prob of 2 and 5/6 us prob of any other except 2, and this needs to be multiplied by 4!/3! as we need arrangement of 4, but since 3 items among the 4 are same we will have to divide by 3!

now Prob (of 2 for 4 times) = 1/6 * 1/6 * 1/6 *1/6

now add them you will get the result. I m quite bad in explaining the things, letme know if you got else I will try another way to explain you.

ekinwang · Answer

Thanks, that was a very good explanation, very easily understood!

achiever01 · Answer

Got my answer, thanks!

aiming4mba · Answer

Gurpreet, well explained. Thanks. Got it now.

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