Question

charlie and clare are playing a number - guessing game. charlie picked two numbers between 1 and 5. to win the game, clare must guess both his numbers in three tries. her guesses, simulated using a random - number generator, are shown in the table. if charlies numbers are 1 and 3, what is the experimental probability that clare won?

Explanation:

Step1: Identify winning trials

A trial is a win if both 1 and 3 are in the set of three - guessed numbers.

Step2: Count total trials

The total number of trials is $n = 10$.

Step3: Count winning trials

The winning trials are: $(5,2,3)$, $(3,4,1)$, $(1,3,3)$, $(1,4,3)$. So the number of winning trials $m=4$.

Step4: Calculate experimental probability

The experimental probability $P=\frac{m}{n}$. Substituting $m = 4$ and $n = 10$, we get $P=\frac{4}{10}=\frac{2}{5}$.

Answer:

$\frac{2}{5}$