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Analyzing a Probability Experiment

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Please help show me how to do a tree diagram for this problem and proving step-by-step solution to make sure the rest of the problem is correct.

14. Suppose you perform a probability experiment in which you toss a fair coin and then roll a fair number cube with the faces labeled with numbers 1 through six.

a. Draw a tree diagram to show all of the outcomes for this experiment. How many outcomes are in the sample space?

b. Calculate the probability that the coin will show heads and the number cube will show a three.
1/2= 0.5 or 50 %; 1/6=0.1667 or 16.67%

c. Calculate the probability that the coin will show tails and the number cube will show an odd number.
1/2=0.5=50%; 3/6=1/2=0.5 or 50%

d. Are all the outcomes equally likely? Explain.
For the coin toss there is an equal chance because you can only roll heads or trail. For the number cube, you have six different outcomes.

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Solution Summary

The solution gives detailed steps on analyzing a probability experiment in which you toss a fair coin and then roll a fair number cube with the faces labeled with numbers 1 through six. A tree diagram is drawn and some probabilities are calculated.

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Please see attached file for full solution.

a. Draw a tree diagram to show all of the outcomes for this experiment. How many outcomes are in the sample space?

See attachment.

So there are 2*6=12 outcomes.
b. ...

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