SOLUTION: 1) 4-card hand is drawn from a standard deck of 52 playing cards. Find the probability that the hand contains the given cards. exactly 4 clubs 2)The Sad State Lottery require

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Question 926547: 1) 4-card hand is drawn from a standard deck of 52 playing cards. Find the probability that the hand contains the given cards.
exactly 4 clubs
2)The Sad State Lottery requires you to select a sequence of four different numbers from 0 through 68. (Order is important.) You are a winner if your sequence agrees with that in the drawing, and you are a booby prize winner if your selection of numbers is correct, but in the wrong order. (Enter your answers as exact answers.)
What is the probability that you are either a winner or a booby prize winner?

I got 1/20748024 for probability of winning and 1/902088 for booby prize probability.
3)Eight white socks and five red socks are in a drawer. If two socks are selected at random, what is the probability that both socks are the same color?
4)An unbiased coin is tossed six times. Find the probability of the given event. (Enter your answer to five decimal places.)
The coin lands heads exactly once.

THANK YOU!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1) 4-card hand is drawn from a standard deck of 52 playing cards. Find the probability that the hand contains the given cards.
exactly 4 clubs
# of ways to succeed:: 13C4
# of possible outcomes:: 52C4
P(4 clubs) 13C4/52C2 = 0.0026
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2)The Sad State Lottery requires you to select a sequence of four different numbers from 0 through 68. (Order is important.) You are a winner if your sequence agrees with that in the drawing, and you are a booby prize winner if your selection of numbers is correct, but in the wrong order. (Enter your answers as exact answers.)
What is the probability that you are either a winner or a booby prize winner?
P(win or boob) = P(win) + P(boob) = 1/69P4 + 1/69C4
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I got 1/20748024 for probability of winning and 1/902088 for booby prize probability.
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3)Eight white socks and five red socks are in a drawer. If two socks are selected at random, what is the probability that both socks are the same color?
P(2 same) = P(2white) + P(2red) = [8C2 + 5C2]/13C2
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4)An unbiased coin is tossed six times. Find the probability of the given event. (Enter your answer to five decimal places.)
The coin lands heads exactly once.
P(x = 1) = 6C1(1/2)^6 = 6/64 = 3/32 = 0.09375
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Cheers,
Stan H.