Lesson: Challenging Problem Solving - 29t01

Advanced Probability: Practice

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A fair coin is tossed 4 times. What is the probability that the coin landed heads up exactly 3 times?

By drawing out the possible tosses, we find that there are four 3 head/1 tail outcomes:

H-H-H-T
T-H-H-H
H-T-H-H
H-H-T-H

Since each of the 4 tosses can be either heads or tails, we can calculate the number of possible outcomes as follows:
2 2 2 2 = 16.

We have four 3 head/1 tail outcomes and 16 possible outcomes, so our probability fraction is

We can also calculate the probabilities for each desired outcome:

Possible Combinations 3 Head/1 Tail	Probability of Each Toss	Combined Probability
H H H T		=
T H H H		=
H T H H		=
H H T H		=
Probability of tossing 2 tails on 3 tosses:		=

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