Question

b) if you flip a coin twenty times and get heads fourteen times: what is the experimental probability of getting heads? what is the experimental probability of getting tails? what is the theoretical probability of getting heads?

Explanation:

Step1: Calculate experimental probability of heads

The experimental probability $P(E)$ is given by the formula $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the number of times heads appeared is 14 and the total number of flips is 20. So, $P(\text{heads})=\frac{14}{20}=\frac{7}{10}$.

Step2: Calculate experimental probability of tails

The number of times tails appeared is $20 - 14=6$. Using the experimental - probability formula, $P(\text{tails})=\frac{6}{20}=\frac{3}{10}$.

Step3: Calculate theoretical probability of heads

For a fair coin, the theoretical probability of getting heads is $\frac{1}{2}$ since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (heads).

Answer:

Experimental probability of heads: $\frac{7}{10}$
Experimental probability of tails: $\frac{3}{10}$
Theoretical probability of heads: $\frac{1}{2}$