Hi! I really need help with this problem, if you could show work so I could foll

Question

Hi! I really need help with this problem, if you could show work so I could follow along I would greatly appreciate it! Thanks in advance!

4.9 Suppose a bowl has 9 chips; one chip is labeled "l. three chips are labeled 3, and five chips are labeled "5". Suppose two chips are selected at random with replacement. Let the random variable X equal the absolute difference between the two draws (e.g. if the first draw is a 1 (11) and the second draw is a 5 (52), then the abeolute difference is 1- (a) Find the probability distribution of X. b) Find the probability that both draws are the same. e)ind the probability that both draws are not the same

Explanation / Answer

here probability that absolute differnce is 0 =P(X=0)=P( both draws have 1+both draws have 3+both draws have 5)

=(1/9*1/9+3/9*3/9+5/9*5/9)=35/81

P(X=2) =P(first draw 1 and second draw 3+first draw 3 and second draw 1+first draw 3 and second draw 5+first draw 5 and second draw 3)

=(1/9*3/9+3/9*1/9+3/9*5/9+5/9*3/9)=36/81

P(X=5) =P(first draw 1 and second draw 5+first draw 5 and second draw 1)=(1/9*5/9+5/9*1/9)=10/81

therefore below is probability distribution:

b) probability =P(X=0)=35/81

c)probability =1-P(X=0)=1-35/81=46/81

d)P(X=2|X>0)=(36/81)/(46/81)=36/46

please revert for any calrification required

x P(x) 0 35/81 2 36/81 4 10/81

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