Please show all work. Thank you so much! 1. What is the probability that a fair

Question

Please show all work. Thank you so much!

1. What is the probability that a fair coin lands on heads exactly five times out of six flips?

2. Suppose you draw three cards in a row from a standard deck without replacement. (a) What is the probability that all three cards are hearts? (b) What is the probability that all three cards are different kinds?

3. Suppose you select a string of six decimal digits at random. (a) What is the probability that the first four digits of the string are 1234? (b) What is the probability that the string does not have a 9 in it?

4. Suppose a lottery game requires that you select five distinct numbers from the first 45 positive integers. (a) What is the probability that none of your five numbers match any of the five winning numbers? (b) What is the probability that you get exactly two of the five numbers right?

Explanation / Answer

We are allowed to do 1 question at a time. Post again for second question.

1) P(Head) = 0.5

P(H = 5) = 6C5 * 0.5^5 * 0.5^1

P = 0.09375

A binomial experiment is a statistical experiment that has the following properties:

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