Discrete random variables and probabilities (1) In a drawer there are five brown

Question

Discrete random variables and probabilities (1) In a drawer there are five brown socks and three green socks. Our experiment is to selected at random two socks and removed in succession from this drawer (a) List the elements of the sample space (b) List the corresponding probabilities for each element of the sample space (c) List the corresponding values w of the random variable W. where W is the number of brown socks selected Hint: Make a table with three columns and 4 rows. In each row you add an element of the sample space the probability of that element and the number of brown socks that this realization has.

Explanation / Answer

a) let brown socks is represented by B and Green by G

therefore sample space space contains these 4 elements ={ BB , BG ,GB, GG}

b) probability of BB =P( first socks is brown and second is brown) =(5/8)*(4/7)=20/56

probability of BG =P( first socks is brown and second is green) =(5/8)*(3/7)=15/56

probability ofGB =P( first socks is green and second is brown) =(3/8)*(5/7)=15/56

probability ofGG =P( first socks is green and second is green) =(3/8)*(2/7)=6/56

c) from above for element BB ; varible W has value w=2 (as there are 2 brown socks)

for element BG ; varible W has value w=1 (as there is 1 brown socks out of 2)

for element GB ; varible W has value w=1 (as there is 1 brown socks out of 2)

for element GG ; varible W has value w=0 (as there is 0 brown socks out of 2)

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