please answer pleaseee If two cards are chosen from a standard deck of cards one at a time and then placed back in the deck, the probability of choosing two 5s is

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02-06-2021
Mathematics

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please answer pleaseee If two cards are chosen from a standard deck of cards one at a time and then placed back in the deck, the probability of choosing two 5s is

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jimthompson5910 jimthompson5910 · Answer 1 · 2021-06-02T01:01:47+02:00

Answer: 1/169

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Explanation:

For now, let's focus on the probability of getting one "5".

There are 4 of these cards (one of each suit) and 52 total. The probability of getting the card we're after is 4/52 = 1/13.

We can think of it like saying "if we focus on one suit only, then there's a 1 in 13 chance of getting a '5' from this pile".

The probability of getting two "5"s in a row is (1/13)*(1/13) = 1/169 assuming we put the first card back. If the first card is not put back, then we would compute it like so: (4/52)*(3/51). I'll leave it unevaluated for you to try out as practice.

Side note: 1/169 = 0.0059 = 0.59% approximately