Question

Please show work in detail and explain all steps

General: Deck of Cards You draw two cards from a standard deck of 52 cards,
but before you draw the second card, you put the f rst one back and reshuff e the
deck.
(a) Are the outcomes on the two cards independent? Why?
(b) Find P(3 on 1st card and 10 on 2nd).
(c) Find P(10 on 1st card and 3 on 2nd).
(d) Find the probability of drawing a 10 and a 3 in either order.

Answer 1

a)

Yes, since experiment is done with replacement , therefore sample space remains same for both the trails and one trail outcome does not affect outcome of other trail

b)since there are 4 cards of 3 and 4 cards of 10 in a deck of 52

due to independence:

P( 3 on 1st card and 10 on 2nd) =P(3 on 1st card)*P(10 on 2nd card)=(4/52)*(4/52)=1/169

c)

P(10 on 1st card and 3 on 2nd) =P(10 on 1st card)*P(3 on 2nd card)=(4/52)*(4/52)=1/169

d)

probability of drawing a 10 and a 3 in either order =P( 3 on 1st card and 10 on 2nd)+P(10 on 1st card and 3 on 2nd) =1/169+1/169 =2/169