Question

Suppose that you have 5 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement. What is the probability that both cards are green?

1) 0.1
2) 0.2
3) 0.25
4) 0.5

Answer 1

The probability of drawing two green cards without replacement from a shuffled set of 10 cards is 2/9. The provided options do not include the correct answer; hence, there might be an error in the question.

Step-by-step explanation:

The question is asking for the probability of drawing two green cards without replacement from a shuffled set of 5 green and 5 yellow cards total. To find the probability of both cards being green, we calculate the probability of the first card being green and then multiply it by the probability of the second card being green given that the first card drawn was already green.

The probability of drawing the first green card is 5/10, or 1/2, since there are 5 green cards out of a total of 10. Once the first green card has been drawn, there are 4 green cards left and only 9 cards in total. Hence, the probability of drawing a second green card is now 4/9.

To find the combined probability, we multiply these two probabilities: (5/10) * (4/9) = 1/2 * 4/9 = 4/18, which simplifies to 2/9. None of the given options (0.1, 0.2, 0.25, 0.5) matches the calculated probability, so there seems to be an error in the provided options.