If a card is chosen from a standard deck of cards, what is the probability of getting a five or a seven?
4/52
1/26
8/52
1/169
If two cards are chosen from a standard deck of cards, what is the probability of getting a five followed by a seven? (assume replacement of the first card)
1/13 * 1/13
1/13 * 1/12
1/13 + 1/13
¼ + ¼
explain replacement of first card? thx
There are 4 fives and 4 sevens, so we are interested in 8 specific cards
prob(5 or 7) = 8/52 = 2/13
(they should reduce their answers to lowest term fractions)
Prob(5, then a 7) = (4/52)(4/52) = 1/169
(oh, now they reduce the fractions to lowest terms, love the consistency)
"Replacement of the first card" means that after the first card is chosen, it is put back into the deck and then another card is chosen. This allows for the possibility of getting the same card on both draws.
In the case of choosing two cards from a standard deck of cards, the probability of getting a five followed by a seven, assuming replacement of the first card, can be calculated as follows:
The probability of getting a five on the first draw is 4/52 (since there are 4 fives in a deck of 52 cards).
After replacing the first card and shuffling the deck, the probability of getting a seven on the second draw is also 4/52.
Using the multiplication rule for independent events, the probability of both events occurring (getting a five followed by a seven) is (4/52) * (4/52).
Therefore, the correct answer is 1/13 * 1/13.