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(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\\

what is the theoretical probability of selecting a king from a standard deck of 52 playing cards?

the experimental probability of an event is based on the results of an experiment that is repeated many times:
\\p(\text{event}) = \frac{\text{number of times desired event occurs}}{\text{total number of trials}}\\

a coin is tossed 40 times. heads appeared 18 times. find the experimental probability of landing on heads.

Explanation:

Calculate theoretical probability of selecting a king

Using the Theoretical Probability, Favorable Outcomes, and Sample Space knowledge points

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Calculate experimental probability of landing on heads

We identify the components for experimental probability:

1. Number of times the desired event occurs (heads): \(18\)
2. Total number of trials (tosses): \(40\)

We apply the experimental probability formula:

$$ P(\text{heads}) = \frac{\text{number of times desired event occurs}}{\text{total number of trials}} $$

Substitute the values and simplify the fraction:

$$ P(\text{heads}) = \frac{18}{40} = \frac{9}{20} $$

Answer:

Question 1

The theoretical probability of selecting a king from a standard deck of 52 playing cards is <blank>\(\frac{1}{13}\)</blank>.

Question 2

A coin is tossed 40 times. Heads appeared 18 times. Find the experimental probability of landing on heads.
The experimental probability is <blank>\(\frac{9}{20}\)</blank>.