Question

mai conducted an experiment by flipping a fair coin 200 times. the coin landed heads up 110 times. which statement about the coin landing heads up in mais experiment is correct? the experimental probability of the coin landing heads up is \\( \frac { 1 } { 2 } \\) and the theoretical probability of the coin landing heads up is \\( \frac { 11 } { 20 } \\). the experimental probability of the coin landing heads up is \\( \frac { 11 } { 20 } \\) and the theoretical probability of the coin landing heads up is \\( \frac { 11 } { 20 } \\). the experimental probability of the coin landing heads up is \\( \frac { 1 } { 2 } \\) and the theoretical probability of the coin landing heads up is \\( \frac { 1 } { 2 } \\). the experimental probability of the coin landing heads up is \\( \frac { 11 } { 20 } \\) and the theoretical probability of the coin landing heads up is \\( \frac { 1 } { 2 } \\).

Explanation:

Step1: Calculate experimental probability

Experimental probability formula: \(P(\text{event})=\frac{\text{number of times event occurs}}{\text{total number of trials}}\).
Here, number of times coin landed heads up \(n = 110\), total number of trials \(N=200\).
So, experimental probability \(P_{exp}=\frac{110}{200}=\frac{11}{20}\).

Step2: Calculate theoretical probability

For a fair coin, there are 2 possible outcomes (\(H\) - heads, \(T\) - tails).
Theoretical probability formula: \(P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\).
Number of favorable outcomes (getting heads) \(m = 1\), total number of possible outcomes \(M = 2\).
So, theoretical probability \(P_{theo}=\frac{1}{2}\).

Answer:

The experimental probability of the coin landing heads up is \(\frac{11}{20}\) and the theoretical probability of the coin landing heads up is \(\frac{1}{2}\) (the bottom - right option).