Suppose that exactly four people in the class hand back homework without names.

Question

Suppose that exactly four people in the class hand back homework without names. Let's say that I know who these students are, but not which assignment goes with which student. If I randomly hand back homework to each student, what's the probability that I hand back exactly 0 assignments to the correct person? Exactly 1? Exactly 2? Exactly 3? Exactly 4? (Hint: how many ways can you choose which people get their own assignments back? Then, how many ways can you assign the assignments in to everyone else? Or, I guess you could list out all the possible permutations and count them up.) correctly

Explanation / Answer

Soln,

Considering it as binomial distribution

Let the probaility of handing over the correct assignment to the right person or probaility of sucess p =1/2=0.5

and the probaility of faliure q =1-P(sucess)=1-0.5=0.5

as asked in question if rhere 0 correct assignment assignment returned to the right person.

then, P(0 sucess) = nCxpxqn-x

Here , x= no sucess

         nCx = Combination in which sucess can be carried out.

So, P(x=0)= 1*(0.5)0*(0.5)4=0.0625

also, P(x=1)= 4* (0.5)*(0.5)3= 0.25

again P(x=2)= 6*(0.5)2*(0.5)2= 0.375

also again P(x=3)= 4*(0.5)3(0.5)=0.25

simillarly P(x=4)= 1* (0.5)4(0.5)0=0.0625

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