Final answer:
Getting a three is independent of the suit in a deck of cards because the likelihood of drawing a three is not influenced by the suit; each suit has an equal probability of being drawn when a card is selected randomly.
Step-by-step explanation:
The question is whether getting a three is independent of the suit when drawing a card from a well-shuffled deck. The deck in question contains 52 cards, with 13 cards in each of the four suits, which are clubs, diamonds, hearts, and spades. A standard deck includes cards numbered 2 through 10, as well as an ace, jack, queen, and king, in each suit.
a. Yes, getting a three is independent of the suit since the probability of drawing a three is not affected by each specific suit.
In a standard deck of cards, there are four threes: one in each suit of clubs, diamonds, hearts, and spades. Because the deck is well-shuffled, all cards have an equal chance of being drawn, making the event of drawing a card random. Independent events are ones where the outcome of one event does not affect the probability of the other. Since the chance of drawing a three is the same regardless of which suit it might be and because the suit doesn't influence the likelihood of drawing a three, these two events are independent. For any given draw, there is always a 1 in 13 chance of drawing a three because there are four threes among the 52 cards. This probability remains constant regardless of which three (of clubs, diamonds, hearts, or spades) is drawn. Therefore, the answer is Yes, getting a three is independent of the suit.