What's the difference between putting back the probability questions in high school mathematics and not putting them back? Case study.

Let ξ 1 be the number of red balls that bag A touches, and ξ2 be the number of red balls that bag B touches.

Then ξ 1 ~ b (1, 1/5), ξ 2 ~ b (2, 1/5)

P(ξ 1=0)=4/5，P(ξ 1= 1)= 1/5

P(ξ2=0)= 16/25，P(ξ2= 1)=8/25，P(ξ2=2)= 1/25

ξ=ξ 1+ξ2

P(ξ=0)=64/ 125，P(ξ= 1)=48/ 125，P(ξ=2)= 12/ 125，P(ξ=0)= 1/ 125

Bachelor of Religion Education bachelor of religious education

ξ 0 1 2 3

p 64/ 125 48/ 125 12/ 125 1/ 125

eξ= eξ 1+eξ2 = 1 *( 1/5)+2 *( 1/5)= 3/5

(This question requires the second bag to touch two balls, Eξ2≠2/5)

I wish I could help.