A coin is flipped 6 times. Heads and tails are equally likely to occur. Show your work. a) How many outcomes are there that the first two flips are heads or the last two flips are heads (or both)? b) What is the probability of gettting three heads in the first three flips? c) What is the probability of getting three heads given that the first two flips resulted in heads?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A coin is flipped 6 times. Heads and tails are equally likely to occur. Show your work.

a) How many outcomes are there that the first two flips are heads or the last two flips are heads (or both)?

b) What is the probability of gettting three heads in the first three flips?

c) What is the probability of getting three heads given that the first two flips resulted in heads?

d) Now assume the coins is weighted. The probability of flipping heads is now 0.5. What is the probability that you flip exactly three heads if you flip the weighted coin 6 times?

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