PLEASE NEED HELP WITH BOTH THE PROBLEMS! Question Suppose that a binary communic

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PLEASE NEED HELP WITH BOTH THE PROBLEMS!

Question Suppose that a binary communication source transmits a sequence of bits (0 or 1), and each bit is independent with a probability 0.305 that it takes the value O. If you observe a sequence of 15 bits, what is the probability that 5 of those are equal to 1? Round your answer to 4 digits to the right of the decimal. You Answered Correct Answer 0.0034 margin of error+0.0001 Question 2 0/1 pts Suppose we deal 36 cards from a well-shuffled standard deck of playing cards. What is the probability that those 36 cards contain3 Kings and 3 Queens? Round your answer to 4 digits to the right of the decimal. You Answered Correct Answer 01775 margin of error +//0.9001

Explanation / Answer

1. Probability that a bit is 1 = 1 - 0.305 = 0.695

P( 5 bits are 1 out of 15 ) = 15C5 * 0.6955 * (1-0.695)15-5 = 0.0034

b. Number of ways of choosing 36 cards from 52 cards = 52C36

Number of ways of choosing 36 cards with 3 kings and 3 queens = 4C3 * 4C3 * 44C30 (Choose 3 kings from 4, 3 queens from 4 and 30 cards from remaining (52-4-4 = 44) cards)

Probability = 4C3 * 4C3* 44C30 / 52C36 = 0.1775

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