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} what is the theoretical probability of selecting a king from a standard deck of 52 playing cards? done 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} a coin is tossed 40 times. heads appeared 18 times. find the experimental probability of landing on heads. done

Explanation:

First Sub - Question (Theoretical Probability of Selecting a King)

Step1: Identify favorable and total outcomes

A standard deck has 52 cards (total outcomes). There are 4 kings (favorable outcomes).

Step2: Apply theoretical probability formula

Using \( P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \), substitute the values: \( P(\text{king})=\frac{4}{52} \).

Step3: Simplify the fraction

Simplify \(\frac{4}{52}\) by dividing numerator and denominator by 4: \(\frac{4\div4}{52\div4}=\frac{1}{13}\).

Step1: Identify desired occurrences and total trials

Heads appeared 18 times (desired occurrences), and the coin was tossed 40 times (total trials).

Step2: Apply experimental probability formula

Using \( P(\text{event})=\frac{\text{number of times desired event occurs}}{\text{total number of trials}} \), substitute the values: \( P(\text{heads})=\frac{18}{40} \).

Step3: Simplify the fraction

Simplify \(\frac{18}{40}\) by dividing numerator and denominator by 2: \(\frac{18\div2}{40\div2}=\frac{9}{20}\).

Answer:

\(\frac{1}{13}\)

Second Sub - Question (Experimental Probability of Landing on Heads)