Question

20 business cards are placed in a hat, 10 belong to women, 10 belong yo men If 2 cards are drawn at once. what's the probability that the first is a Man's card and the Second, A woman's card?
5/19
14/19
1/4
9/10

Answer 1

Answer:

5/19

Step-by-step explanation:

I know this isn't as good as the other persons answer but I wanted to reassure you that it was correct and my proof is that I took a test on this and got it right with this answer. I hope I helped! :>

Answer 2

Answer:

First choice:

               $\large\boxed{\large\boxed{5/19}}$

Explanation:

The probability that the first is a man's card and the second, a woman's card is calculated as the product of both probabilities, taking into account the fact that the second time the number of cards  in the hat has changed.

In spite of it is said that the cards are drawn at once, since it is stated a specific order for the cards (first is a man's card and the second, a woman's card) you can model the procedure as if the cards were drawn consecutively, instead of at once.

1. Probability that the first is a man's card

• Number of cards in the hat = 20 (the 20 business card)

• Number of man's card in the hat: 10

• Probability = favorable oucomes / possible outcomes = 10/20 = 1/2.

2. Probability that the second is a woman's card

• Number of cards in the hat = 19 (there is one less card in the hat)

• Number of wonan's card in the hat: 10

• Probability = favorable oucomes / possible outcomes = 10/19.

3. Probability that the first is a man's card and the second, a woman's card

• (1/2) × (10/19) = 5/19

That is the first choice.