SOLUTION: Please show steps of how to solve the question. 1 ) You are dealt a hand of four cards, one at a time. (Round your answers to nearest whole percent) Determine the probability

Question 1203214: Please show steps of how to solve the question.
1 ) You are dealt a hand of four cards, one at a time.
(Round your answers to nearest whole percent)
Determine the probability of the following events:
a) Only the second card is a Spade.
Probability is: %
b) All 4 cards are Red.
Probability is: %
c) None of the cards are Clubs.
Probability is: %
d) At least 1 card is a Queen.
Probability is: %
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
1 ) You are dealt a hand of four cards, one at a time.
(Round your answers to nearest whole percent)
Determine the probability of the following events:

these are all without replacement.

a) Only the second card is a Spade.
Probability is: %

there are 13 spades in the deck that are spades and 39 cards in the deck that are not spades, out of a total of 52.

the probability of getting a spade on the second draw only is 39/52 * 13/51 * 38/50 * 37/49 = .1097118848.
multiply by 100 to get percent and round as required.

b) All 4 cards are Red.
Probability is: %

there are 26 red cards in the deck and 26 black cards, out of a total of 52.
the red cards are hearts and diamonds.
the black cards are clubs and spades.

probability of getting 4 cards that are red is 26/52 * 25/51 * 24/50 * 23/49 = .0552220888.
multiply by 100 to get percent and round as required.

c) None of the cards are Clubs.
Probability is: %

there are 13 cards in the deck that are clubs and 39 cards in the deck that are not clubs, out of a total of 52.

probability of getting 4 cards that are not clubs is 39/52 * 38/51 * 37/50 * 36/49 = .303817527.
multiply by 100 to get percent and round as required.

d) At least 1 card is a Queen.
Probability is: %

there are 4 cards in the deck that are queens and 48 cards in the deck that are not queens, out of a total of 52.

the probability of getting at least 1 queen is 1 minus the proability of getting 0 queens.

the probability of getting 0 queens out of 4 tries is 48/52 * 47/51 * 46/50 * 45/49 = .7636577708.
the probability of getting at least 1 queen is 1 minus that = .2363422292.
multiply by 100 to get percent and round as required.

i'm pretty sure this is correct.
check it out and let me know what you think.

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