Question

Emil would like to estimate the probability of 2 or more heads coming up in 3 coin flips. To do this, he has a computer randomly select 0 or 1 three times, with 0 representing heads and 1 representing tails. The results of 12 trials are shown in the table. 111 011 000 010 100 111 010 111 111 101 000 111 What is Emil's estimated probability, based on this simulation? Enter your answer as a fraction, in simplified form, in the box.

Answer 1

Probability helps us to know the chances of an event occurring. Emil's estimated probability, based on this simulation is 0.4167.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

As it is given that if the output of the computer is 1, then it represents tails, while the 0 represents the head. Also, the results of 12 trials are 111, 011, 000, 010, 100, 111, 010, 111, 111, 101, 000, 111.

Now, in the set of results, we need to calculate the number of results in which the outcome is 2 or more heads, therefore, we need the output that has 2 or more zeroes in it.

Results with 2 or more zeroes are 000, 010, 100, 010, 000

The number of results with 2 or more zeroes is 5.

The total number of possible results is 12.

The probability That Emil will get 2 or more heads can be written as,

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

$\rm Probability(2\ or\ more\ zero) = \dfrac{\text{Number of results with 2 or more zeroes }}{\text{Total number of possible results }}$

$\rm Probability(2\ or\ more\ zero) = \dfrac{5}{12} = 0.4167 = 41.67\%$

Hence, Emil's estimated probability, based on this simulation is 0.4167.

Learn more about Probability:

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