Question

Letter FrequencyHakeem randomly draws equal-sized cards labeled with letters A, B,C, D, and F from a hat and records the results in the table. Comparethe theoretical and experimental probabilities of randomly drawinga card that is labeled with the letter C.А36B50с111D59LLF44Total3003 7-3 Understand Experimental ProbabilityGo Online PearsonRealize

Answer 1

Step-by-step explanation:

Given;

We are told that randomly draws equal sized cards labeled A, B, C, D and F. Also he carries out an experiment where he draws a card randomly 300 times. The frequency of drawing each different type of card is recorded as shown in the table.

Required;

We are required to calculate the experimental and theoretical probabilities of randomly drawing a card labeled C.

Step-by-step solution;

We need to begin by explaining the difference between the experimental probability and the theoretical probability.

For a theoretical probability, the likelihood of an event occurring is a prediction based on mathematical models. That is;

`P[Event]=\frac{Number\text{ }of\text{ }required\text{ }outcomes}{Number\text{ }of\text{ }all\text{ }possible\text{ }outcomes}`

In other words, this formula helps to predict the probability in theory. The actual outcome might be slightly different or likely exactly as predicted.

However, for an experimental probability, we take a look at predictions based on the results of experiments that have been carried out successfully.

Hence, when we have 5 equally sized cards in a hat, the probability of drawing any of them will be equally likely.

This means in theory each card stands a one out of five chance of being drawn.

What we now have is;

Theoretical Probability of drawing a card labeled C;

`\begin{gathered} P[C]=(1)/(5) \\ P[C]=0.2 \end{gathered}`

For an experiment where cards were drawn 300 times and the card labeled C came up 111 times,

Experimental Probability of drawing a card labeled C;

`\begin{gathered} P[C]=(111)/(300)=(37)/(100) \\ \\ P[C]=0.37 \end{gathered}`

ANSWER:

Therefore, we can conclude that from the results of this experiment, the experimental probability of drawing card C is greater than the theoretical probability of drawing card C.

`\begin{gathered} Theoretical\text{ }probability=0.2 \\ \\ Experimental\text{ }probability=0.37 \end{gathered}`