Using a standard 52-card deck, find the following probabilities. Leave your answer as a reduced fraction. If a card is randomly selected, what is the probability that the card is any one suit, e.g., a diamond, heart, spade, or club? If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card? Hint: There are 12 face cards, and 40 numbered cards in a standard deck of cards.

Sure, let's solve these problems step by step.

1. If a card is randomly selected, what is the probability that the card is any one suit, e.g., a diamond, heart, spade, or club?

A standard deck of 52 cards is divided into 4 suits: diamonds, hearts, spades, and clubs. So, there are 52/4 = 13 cards of each suit.

The probability of drawing any one suit is therefore the number of ways to draw one card of that suit divided by the total number of possible outcomes, i.e., the total number of cards in the deck.

So, the probability P(Diamond OR Heart OR Spade OR Club) = 13/52 = 1/4.

2. If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card?

First, let's find the probability of drawing any one suit. As we found in the previous question, this is 1/4.

Next, let's find the probability of drawing a face card. There are 12 face cards in a deck of 52 cards, so the probability is 12/52 = 3/13.

However, since we've already drawn one card (the first card of any suit), there are now only 51 cards left in the deck. So, the probability of drawing a face card after drawing the first card is 12/51.

The probability of both events happening is the product of their individual probabilities. So, the probability P(Any suit first AND face card second) = (1/4) * (12/51) = 3/51 = 1/17.