Question

which statements are true about the experimental and theoretical probability of this trial?
jacobs coin flips
outcome heads tails
frequency 68 32
the theoretical probability of landing heads up is less than the experimental probability of landing heads up.
the experimental probability of landing tails up is less than the theoretical probability of landing tails up.
the experimental probability of landing heads up is less than the experimental probability of landing tails up.
the experimental probability of landing heads up is equal to the theoretical probability of landing heads up.

Explanation:

Step1: Calculate total number of flips

$68 + 32=100$

Step2: Calculate theoretical probability of heads

For a fair - coin, the theoretical probability of getting heads, $P_{theo}(H)=\frac{1}{2}=0.5$

Step3: Calculate experimental probability of heads

$P_{exp}(H)=\frac{68}{100} = 0.68$

Step4: Calculate theoretical probability of tails

For a fair - coin, the theoretical probability of getting tails, $P_{theo}(T)=\frac{1}{2}=0.5$

Step5: Calculate experimental probability of tails

$P_{exp}(T)=\frac{32}{100}=0.32$

Step6: Analyze statements

• The theoretical probability of landing heads up ($0.5$) is less than the experimental probability of landing heads up ($0.68$), so the statement "The theoretical probability of landing heads up is less than the experimental probability of landing heads up" is true.
• The experimental probability of landing tails up ($0.32$) is less than the theoretical probability of landing tails up ($0.5$), so the statement "The experimental probability of landing tails up is less than the theoretical probability of landing tails up" is true.
• The experimental probability of landing heads up ($0.68$) is greater than the experimental probability of landing tails up ($0.32$), so the statement "The experimental probability of landing heads up is less than the experimental probability of landing tails up" is false.
• The experimental probability of landing heads up ($0.68$) is not equal to the theoretical probability of landing heads up ($0.5$), so the statement "The experimental probability of landing heads up is equal to the theoretical probability of landing heads up" is false.

Answer:

The theoretical probability of landing heads up is less than the experimental probability of landing heads up.
The experimental probability of landing tails up is less than the theoretical probability of landing tails up.