5. a circle then a heart is chosen 4 out of 50 times from the cards shown. find the experimental…

Explanation:

Step1: Calculate experimental probability

The experimental - probability formula is $P=\frac{\text{number of favorable outcomes}}{\text{total number of trials}}$. Here, the number of favorable outcomes is 4 and the total number of trials is 50. So, $P_{exp}=\frac{4}{50}=\frac{2}{25}=0.08$.

Step2: Calculate theoretical probability

There are 4 cards. The probability of choosing a circle first is $\frac{1}{4}$, and the probability of choosing a heart second (assuming replacement, since no information about non - replacement is given) is $\frac{1}{4}$. By the multiplication rule for independent events, $P_{theo}=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}=0.0625$.

Step3: Compare probabilities

Since $0.08>0.0625$, the experimental probability is greater than the theoretical probability.

Answer:

Experimental probability: $\frac{2}{25}$ or 0.08; Theoretical probability: $\frac{1}{16}$ or 0.0625; The experimental probability is greater than the theoretical probability.