Question

A problem in a test given to small children asks them to match each of three pictures of animals to the word identifying that animal. If a child assigns the three words at random to the three pictures ,Find the probability distribution for Y , the number of correct matches.

Answer 1

Solution

Find the probability distribution for Y 

Y: The number of correct matches: $Y=0,1,3$

Let C: Correct, I : Incorrect

$\oplus\hspace{2mm} Y=0 : \Big\{(III)\Big\}$

$\implies P(Y=0)=\frac{2}{3}\times \frac{1}{2}=\frac{1}{3}$

$\oplus\hspace{2mm} Y=1 : \Big\{(CII),(ICI),(ICI)\Big\}$

$\implies P(Y=1)=3\times\frac{1}{3}\times \frac{1}{2}=\frac{1}{2}$

$\oplus\hspace{2mm} Y=3 : \Big\{(CCC)\Big\}$

$\implies P(Y=3)=\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$

 

 

Therefore.