Question

MEDAL!!

(refer to choosing two cards from a thoroughly shuffled deck. Assume that the deck is shuffled after a card is returned to the deck)

If you put the first card back in the deck before you draw the next, what is the probability that the first card is a 10 and the second card is a jack?

Answer 1

Focus on one card at a time. What is the probability of pulling out a "10" card ?

Answer 2

here's a visual of all the cards (52 total; 4 suits, 13 per suit)

http://www.jfitz.com/cards/classic-playing-cards.png

Answer 3

hmm, there are four 10s

Answer 4

yes, so the probability of picking a single 10 is?

Answer 5

guessing 4 out of 52

Answer 6

you can reduce that fraction to get ?

Answer 7

4/52 = ???

Answer 8

1/13

Answer 9

yes

Answer 10

so if you focus on one suit only, there is a 1 in 13 chance to get a "10" card

Answer 11

next step: find the probability of picking a jack. All 52 cards are still there since the first card was put back (it says `Assume that the deck is shuffled after a card is returned to the deck`)

Answer 12

if there are 4 jacks wouldn't it be 4/52=1/13 again?

Answer 13

yep

Answer 14

now multiply the two fractions

Answer 15

P(10 on first draw, jack on second draw) = P(10 on first draw) * P(jack on second draw)

this works because the two events are independent

Answer 16

multiplying the two fractions would get me 1/169

Answer 17

which is the correct final answer

Answer 18

thanks again jim!