Question

the theoretical probability of an event is the number of ways an event can occur divided by the total number of possible outcomes: $p(event)=\frac{number of favorable outcomes}{total number of possible outcomes}$ the experimental probability of an event is based on the results of an experiment that is repeated many times: $p(event)=\frac{number of times desired event occurs}{total number of trials}$ what is the theoretical probability of selecting a king from a standard deck of 52 playing cards? a coin is tossed 40 times. heads appeared 18 times. find the experimental probability of landing on heads.

Explanation:

Step1: Find number of favorable outcomes and total outcomes for theoretical probability

A standard deck has 52 cards. There are 4 kings (favorable outcomes). Total number of possible outcomes is 52.

Step2: Calculate theoretical probability

Using the formula \(P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\), we have \(P(\text{selecting a king})=\frac{4}{52}=\frac{1}{13}\)

Step3: Find number of times desired event occurs and total number of trials for experimental probability

Number of times desired event (heads) occurs is 18. Total number of trials (coin - tosses) is 40.

Step4: Calculate experimental probability

Using the formula \(P(\text{event})=\frac{\text{number of times desired event occurs}}{\text{total number of trials}}\), we have \(P(\text{landing on heads})=\frac{18}{40}=\frac{9}{20}\)

Answer:

The theoretical probability of selecting a king is \(\frac{1}{13}\). The experimental probability of landing on heads is \(\frac{9}{20}\)