Question

1. cards draw one card from a standard 52 - card deck 40 times with replacement and compute the empirical probability of selecting a heart.

Explanation:

Step1: Determine number of hearts in deck

A standard 52 - card deck has 13 hearts.

Step2: Calculate theoretical probability of drawing a heart

The probability of drawing a heart in a single draw from a 52 - card deck is $P=\frac{13}{52}=\frac{1}{4}$.

Step3: Conduct the experiment

We draw a card 40 times with replacement. Let $n$ be the number of times a heart is drawn. In theory, if the experiment follows the theoretical probability, we expect $n = 40\times\frac{1}{4}=10$ times.

Step4: Calculate empirical probability

The empirical probability $P_{empirical}=\frac{n}{40}$. If we assume we get $n$ hearts in 40 draws, say we actually draw 12 hearts in the 40 draws (this number can vary in actual experiments), then $P_{empirical}=\frac{12}{40}=\frac{3}{10} = 0.3$.

Answer:

The empirical probability depends on the actual number of times a heart is drawn in 40 draws. If we assume we draw 12 hearts in 40 draws, the empirical probability is 0.3.