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?

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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?

Mathematics
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Focus on one card at a time. What is the probability of pulling out a "10" card ?
here's a visual of all the cards (52 total; 4 suits, 13 per suit) http://www.jfitz.com/cards/classic-playing-cards.png
hmm, there are four 10s

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yes, so the probability of picking a single 10 is?
guessing 4 out of 52
you can reduce that fraction to get ?
4/52 = ???
1/13
yes
so if you focus on one suit only, there is a 1 in 13 chance to get a "10" card
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`)
if there are 4 jacks wouldn't it be 4/52=1/13 again?
yep
now multiply the two fractions
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
multiplying the two fractions would get me 1/169
which is the correct final answer
thanks again jim!

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