Question

suit observed frequency clubs 29 spades 13 hearts 15 diamonds 23 how does the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart? the theoretical probability of choosing a heart is 1/16 greater than the experimental probability of choosing a heart. the experimental probability of choosing a heart is 1/16 greater than the theoretical probability of choosing a heart. the theoretical probability of choosing a heart is 1/26 greater than the experimental probability of choosing a heart. the experimental probability of choosing a heart is 1/26 greater than the theoretical probability of choosing a heart.

Explanation:

Step1: Calculate total observed frequency

$29 + 13+15 + 23=80$

Step2: Calculate experimental probability of choosing a heart

Experimental probability $P_{exp}=\frac{15}{80}=\frac{3}{16}$

Step3: Calculate theoretical probability of choosing a heart

In a standard deck of 52 cards, there are 13 hearts. Theoretical probability $P_{theo}=\frac{13}{52}=\frac{1}{4}=\frac{4}{16}$

Step4: Find the difference

$P_{theo}-P_{exp}=\frac{4}{16}-\frac{3}{16}=\frac{1}{16}$

Answer:

The theoretical probability of choosing a heart is $\frac{1}{16}$ greater than the experimental probability of choosing a heart.