a straight in five - card poker is five cards...
a straight in five - card poker is five cards with consecutive denominations. if youre dealt $j, q, k, a$, and a queen, then discard the queen and draw one card to replace it, whats the probability of getting a straight or a pair? assume that all other cards are still in the deck. express your answer as a fraction in simplest form.\nthe probability that you will get a straight or a pair is (square)
Answer
# Explanation:
## Step1: Calculate total number of possible draws
There are 52 - 4 = 48 cards left in the deck (since we have 4 cards in - hand and are discarding 1, so 52-(4 + 1)=48). So the total number of possible outcomes when drawing 1 card is 48.
## Step2: Calculate number of cards that give a straight
To get a straight, we need a 10 or a 2. There are 4 tens and 4 twos in a standard deck. So there are 4 + 4=8 cards that can complete a straight.
## Step3: Calculate number of cards that give a pair
We have a J, Q, K, A in - hand. There are 3 jacks, 3 kings, and 3 aces left in the deck that can give us a pair. So there are 3+3 + 3=9 cards that can give a pair.
## Step4: Calculate number of favorable outcomes
We need to be careful not to double - count. The events of getting a straight and getting a pair are mutually exclusive in this case. So the number of favorable outcomes is 8 + 9=17.
## Step5: Calculate the probability
The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P = \frac{17}{48}$.
# Answer:
$\frac{17}{48}$