Assume that the coins are fair. If a sample point is the result of n t

kzae220o3 2021-11-22 Answered
Assume that the coins are fair. If a sample point is the result of n tosses, assign a probability of \(\displaystyle{\left({\frac{{{1}}}{{{2}}}}\right)}^{{{n}}}\) to that sample point. Verify that the probability of the whole sample space is 1. Calculate the probability that the second toss results in heads.

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Expert Answer

Florence Pittman
Answered 2021-11-23 Author has 1186 answers
Step 1
(b) Given that the coin is fair
Therefore, the probability of head and tail for the coin is same which is 12.
The sample space for the a coin tossed is:
\[\begin{array}{|c|c|} \hline Outcome & head&tails \\ \hline Probability&\frac{1}{2}&\frac{1}{2} \\ \hline \end{array}\]
Determine the probability of whole sample space.
\(\displaystyle{P}={\frac{{{1}}}{{{2}}}}+{\frac{{{1}}}{{{2}}}}\)
\(\displaystyle={1}\)
Therefore, it is verified that the probability of whole sample space is 1.
Step 2
Determine the probability of head.
\(\displaystyle{p}={\frac{{\text{favourable outcome}}}{{\text{Total outcome}}}}\)
Substitute the respective values.
\(\displaystyle{p}={\frac{{{1}}}{{{2}}}}\)
Therefore, the probability of heads is \(\displaystyle{\frac{{{1}}}{{{2}}}}\).
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