Express each ratio as a fraction in the simplest form
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A standard deck of playing cards consists of 52 playing cards.
1. Count the probability of drawing two aces from a standard deck without replacment.
Among 52 playing cards are 4 aces, then the probability to select first ace is 4/52=1/13. After picking out first ace, only 3 aces left and in total 51 playing cards left, then the probability to select second ace is 3/51=1/17. Use the product rule to find the probability to select two aces without replacement:
2. Count the probability of drawing two aces from a standard deck with replacment.
Among 52 playing cards are 4 aces, then the probability to select first ace is 4/52=1/13. After picking out first ace, this card was returned back into the deck and the probability to select second ace is 4/52=1/13 too. Use the product rule to find the probability to select two aces with replacement:
3. If events A and B are independent, then
All these three steps show you that the first card was replaced and events are independent.