SOLUTION: Q:1 A card is drawn from a deck of 52 cards,then replaced and a second card is drawn 1)What is the probability of drawing same card twice? 2)What is the probability of drawing

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Question 483545: Q:1 A card is drawn from a deck of 52 cards,then replaced and a second card is drawn
1)What is the probability of drawing same card twice?
2)What is the probability of drawing a 3 of hearts and then a 4 of spades?
3)Calculate above mentioned probabilities if first card is not replaced?
Q:2 A information source produces 0's and 1's with probabilities of 0.3 and 0.7 respectively.The output of the source is transmitted via channel that has a probability of error(turning 1 into 0 and 0 into 1 ) equal to 0.2
1) What is the probability that at the output a 1 is observed .
2) What is the probability that a 1 was the output of the source if the output of the channel a 1 is observed.
Answer by stanbon(75887) (Show Source):
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Q:1 A card is drawn from a deck of 52 cards,then replaced and a second card is drawn
1)What is the probability of drawing same card on the 2nd draw?:: (1/52)
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2)What is the probability of drawing a 3 of hearts and then a 4 of spades?
:: (1/52)^2
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3)Calculate above mentioned probabilities if first card is not replaced?
:: 0 and (1/52)(1/51)
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Q:2 An information source produces 0's and 1's with probabilities of 0.3 and 0.7 respectively.
The output of the source is transmitted via channel that has a probability of error(turning 1 into 0 and 0 into 1 ) equal to 0.2
1) What is the probability that at the output a 1 is observed.::0.7
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2) What is the probability that a 1 was the output of the source if the output of the channel a 1 is observed.:: P(1 | 1 transmitted) = 0.8
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Cheers,
Stan H.