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? __ 3. which fraction is greater, $\frac{6}{7}$ or $\frac{3}{5}$? show your work and explain how you know.

Explanation:

Step1: Calculate experimental probability of heads

The experimental probability $P(H)$ of getting heads is the number of times heads occurred divided by the total number of flips. Given heads occurred 14 times and total flips are 20. So $P(H)=\frac{14}{20}=\frac{7}{10}$.

Step2: Calculate experimental probability of tails

The number of tails is $20 - 14=6$. The experimental probability $P(T)$ of getting tails is the number of times tails occurred divided by the total number of flips. So $P(T)=\frac{6}{20}=\frac{3}{10}$.

Step3: Determine theoretical probability of heads

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

Step4: Compare fractions $\frac{6}{7}$ and $\frac{3}{5}$

Find a common denominator. The common denominator of 7 and 5 is $7\times5 = 35$. Rewrite the fractions: $\frac{6}{7}=\frac{6\times5}{7\times5}=\frac{30}{35}$ and $\frac{3}{5}=\frac{3\times7}{5\times7}=\frac{21}{35}$. Since $\frac{30}{35}>\frac{21}{35}$, then $\frac{6}{7}>\frac{3}{5}$.

Answer:

Experimental probability of heads: $\frac{7}{10}$
Experimental probability of tails: $\frac{3}{10}$
Theoretical probability of heads: $\frac{1}{2}$
Greater fraction: $\frac{6}{7}$