Question

Of the 16 cards drawn from a standard deck of 52 cards, 5 of the cards are spades. Based on the cards that were drawn, the empirical probability of drawing a spade is ___, and the difference of the empirical and theoretical probabilities of drawing a spade from a standard deck of cards is ___.

A) 0.3125 / 0.25
B) 0.3125 / 0.125
C) 0.3125 / 0.1875
D) 0.375 / 0.25

Answer 1

The empirical probability of drawing a spade from the cards drawn is 0.3125, and the difference between the empirical and theoretical probabilities of drawing a spade is 0.0625, which corresponds to option A.

Step-by-step explanation:

The empirical probability of drawing a spade from the 16 cards is found by dividing the number of spades (5) by the total number of cards drawn (16). This gives us:

Empirical Probability = 5/16 = 0.3125

The theoretical probability of drawing a spade from a standard deck of 52 cards, where there are 13 spades, is:

Theoretical Probability = 13/52 = 0.25

Now, to find the difference between the empirical and theoretical probabilities, we subtract the theoretical probability from the empirical probability:

Difference in Probabilities = 0.3125 - 0.25 = 0.0625

Therefore, the correct answer is option A) 0.3125 / 0.0625.