Question

You flip a coin 100 times in the air and find that it lands on heads 65 times. Determine the theoretical and experimental probability of landing on heads. In your final answer, include all of your calculations.

Answer 1

Answer:

The experimental probability --> $\frac{13}{20}$

The theoretical probability --> $\frac{1}{2}$

Step-by-step explanation:

Key skills needed: Experimental vs theoretical probability, Fractions

1) The first thing you need to understand is experimental probability vs theoretical probability. (Do not include this in your work!!)

- Theoretical probability is based on simple reasoning

- Experimental probability is based on the results a person gets (so the experiment you did by flipping the coin)

2) Now with this, let's start solving:

1. Experimental probability ---> $\frac{heads}{total}$ -->  You flipped the coin  a total of 100 times, so the denominator would be 100. 65 of those would be heads so 65 is our numerator.
2. So our experimental probability is --> $\frac{65}{100}$ --> Both have the factor of 5, so take the factor of 5 out of the numerator and denominator and you will get --> $\frac{13}{20}$
3. Now onto theoretical probability --> $\frac{heads}{total}$ --> There are 2 faces of a coin, 1 side is heads, and 1 side is tails --> The total number of faces is 2, so 2 is our denominator. There is only 1 side that is heads, so 1 is the numerator. This means  --> Our theoretical probability is $\frac{1}{2}$

Hope you understood and have a nice day!! :D

Answer 2

Answer:

Experimental Probability: 65/100 We tested the probability 100 times, 65 of those times being heads. So %65 is our experimental probability (in percentage form) of flipping a coin and landing on heads. Simplified, 13/20 is our fraction.

Theoretical Probability: 50/100 or 1/2. There are two sides to a coin, and one is heads, so the theoretical probability is 1/2. In percentage form, the probability would be %50, or 50/100.