Hi! I really need help with this problem instead of with replacement I need help

Question

Hi! I really need help with this problem instead of with replacement I need help doing this exact problem WITHOUT replacement, if you could show work so I could follow along I would greatly appreciate it! Thanks in advance!

4.7 Suppose a bowl has 5 chips, two chips are labeled, and three chips are labeled Suppose two chips are selected at random with replacement. Let the random variable X equal the product of the two draws (e.g. if the first draw is a 2 (21) and the second draw is a 3 (32), then the product is 2x3=6) (a) Find the probability distribution of X (b) Find the probability that the product of the two draws is less than or equal to 6 i.e. find PX s6) (c) Find the probability that the product of the two draws is greater than 4 given that the product is less than or equal to 6, e. find P(X>4X s6) (d) Compute the expected value of X. (e) Compute a SD(x).

Explanation / Answer

a) here P(X=4) =P( first draw is 2 and second draw is 2) =(2/5*2/5) =4/25

P(X=6)=P( first draw is 2 and second 3+first draw is 3 and second 2)=(2/5*3/5+3/5*2/5) =12/25

P(X=9) =P(first draw is 3 and second draw is 3)= (3/5*3/5) =9/25

therfore below is probability distribution of X:

b)P(X<=6) =P(X=2)+P(X=6) =16/25

c)P(X>4|X<=6)=(12/25)/(16/25)=12/16=3/4

d) from above

expected value E(X) =6.76

SD(X)=1.8173

x P(x) 4 4/25 6 12/25 9 9/25

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