Answer:
13 / 204; No, they are dependent events
Explanation:
Total number of cards in the deck = 52
Total number of spades in the deck = 13
Total number of hearts in the deck = 13
Part 1: Calculating the Probability
Picking up the first card:
When picking the first card i.e spade, we have the option to pick 13 cards out of 52. So the probability will be 13/52
When first card is picked, the total number of cards will be reduced to 51 because we are not placing the card back in the deck
Picking up the second card:
When picking up the second card i.e. heart, we have the option to pick 13 cards out of 51. So the probability will be 13/51
The probability of picking a spade and then a heart is = 13/52 x 13/51 = 13/204
Part 2: Independent or Not
Note that, picking up a spade and not replacing it back is changing the probability of picking up a heart. In normal cases, picking up a heart from a deck will have the probability of 13/52, but since the we are not placing the card back the probability is changed to 13/51
Since, the probability of picking a heart is being changed by the previous event, we say that the two events are dependent.
Therefore, the correct answer will be final option: 13 / 204; No, they are dependent events