Identify this probability as independent or dependent

A bag contains ten cards numbered 1 through 10. You pick one card and then another without replacement. What is the probability that both cards display a value of 6 or higher?

My answer: Dependent

There are 5 card which are 6 or higher

so prob(2 of those)
= (5/10)(4/9)
= 2/9

To determine whether the probability is independent or dependent, we need to consider whether the outcome of the first event (picking a card) affects the probability of the second event (picking another card).

In this scenario, the probability is dependent. Here's how to see why:

First, let's find the probability of picking a card with a value of 6 or higher on the first draw. Out of the ten cards, there are five cards with values of 6 or higher (6, 7, 8, 9, and 10). So, the probability of picking such a card on the first draw is 5/10, which can be simplified to 1/2.

After drawing a card, there are nine cards remaining in the bag, and four of them have a value of 6 or higher. So, the probability of drawing another card with a value of 6 or higher on the second draw, given that the first card was already picked, is 4/9.

To find the probability of both events happening (picking a card with a value of 6 or higher on the first draw and another one on the second draw), we multiply the separate probabilities together:

(1/2) × (4/9) = 4/18 = 2/9

Therefore, the probability that both cards display a value of 6 or higher is 2/9. Since the probability of the second event (drawing a card with a value of 6 or higher) is dependent on the outcome of the first event (drawing a card), we can conclude that this probability is dependent.