Final answer:
Mutually exclusive events in card drawing, such as drawing a heart or a spade from a standard deck, are calculated by adding the probabilities of each separate event. Sampling with replacement allows for the same card to be drawn again, while sampling without replacement does not.
Step-by-step explanation:
When you draw one card from a standard deck of playing cards, there are events that are mutually exclusive, such as drawing a heart (H) or a spade (S). These events are mutually exclusive because a card cannot be both a heart and a spade simultaneously. To calculate the probability of drawing a heart or a spade, you simply add the probability of each event since they cannot occur together. There are 13 hearts and 13 spades in a 52-card deck, so the probability of drawing a heart or spade is (13/52) + (13/52) = 1/4 + 1/4 = 1/2 or 50%.
When it comes to sampling with replacement, it implies that after drawing a card, it is placed back into the deck, and the deck is reshuffled before drawing again, which allows for the possibility of drawing the same card more than once. In contrast, sampling without replacement means that once a card is drawn, it is not returned to the deck, reducing the total number of cards for subsequent draws and making it impossible to draw the same card again.