Answer :
Hello there. To solve this question, we'll have to remember some properties about probabilities.
Given that, in a survey with 300 people, they were to choose one card out of 5 labeled 1 to 5 and we get the frequency in the table, we can find the theoretical and experimental probabilities and compare them.
The theoretical probability of taking a card with the number 3 out of 5 is given by the ratio of the number of favorable events and the number of total elements of the sample.
If this amount of cases are considered to be a draw of a card with replacement, we get that:
[tex]P(3)=\mleft(\frac{1}{5}\mright)^{300}[/tex]And we get approximately equal to:
[tex]P(3)\approx2\cdot10^{-210}[/tex]That is, each of the person taking a 3 out of the 5 card deck.
But as we just want the probability of taking a card with the number 3, we simply have:
[tex]P=\frac{1}{5}\text{ or 20\%}[/tex]The experimental probability can be calculated by a very similar ratio, that is, between the frequency the cards are drawn and the number of total draws:
[tex]EP=\frac{84}{300}=\frac{28}{100}=28\%[/tex]This is the experimental probability of choosing a card with the number 3.
