Question

a card is chosen at random from a deck of 24 cards (2 red, 12 black, 4 blue, and 6 green). then, the card is returned to the deck and a new card is chosen. the table below shows cards. for which color of card is the experimental probability the same as the theoretical probability?
results
red black blue green
5 8 1 2
a blue
b black
c red
d green

Explanation:

Step1: Calculate total trials

Sum the experimental results: \(5 + 8 + 1 + 2 = 16\) trials.

Step2: Find theoretical probabilities

• Red: \(\frac{2}{24}=\frac{1}{12}\approx0.083\)
• Black: \(\frac{12}{24}=\frac{1}{2} = 0.5\)
• Blue: \(\frac{4}{24}=\frac{1}{6}\approx0.167\)
• Green: \(\frac{6}{24}=\frac{1}{4}=0.25\)

Step3: Find experimental probabilities

• Red: \(\frac{5}{16}=0.3125\)
• Black: \(\frac{8}{16}=0.5\)
• Blue: \(\frac{1}{16}=0.0625\)
• Green: \(\frac{2}{16}=0.125\)

Step4: Compare probabilities

Black's experimental (\(0.5\)) = theoretical (\(0.5\)).

Answer:

B. black