Question

reviewing computing probability
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?
options: $\frac{1}{13}$, $\frac{1}{4}$, $\frac{4}{13}$, $4$
another problem: a coin is tossed 40 times. heads appeared 18 times. find the experimental probability of landing on heads.

Explanation:

First 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 probability formula

The formula for theoretical probability is \( P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \). Substituting the values, we get \( P(\text{king}) = \frac{4}{52} \).

Step3: Simplify the fraction

Simplify \( \frac{4}{52} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So, \( \frac{4 \div 4}{52 \div 4} = \frac{1}{13} \).

Step1: Recall the experimental probability formula

The formula for experimental probability is \( P(\text{event}) = \frac{\text{number of times the event occurs}}{\text{total number of trials}} \).

Step2: Identify the values

The event (heads) occurred 18 times, and the total number of trials (coin tosses) is 40.

Step3: Apply the formula

Substitute the values into the formula: \( P(\text{heads}) = \frac{18}{40} \).

Step4: Simplify the fraction

Simplify \( \frac{18}{40} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \( \frac{18 \div 2}{40 \div 2} = \frac{9}{20} \).

Answer:

\( \frac{1}{13} \) (corresponding to the option "1/13")

Second Question (Experimental Probability of Landing on Heads):