two cards are drawn from a deck of cards. Once a card is drawn, it is not replaced. Find the probability of drawing a queen followed by a king.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Q = 4/52
K = 4/51
Multiply.
To find the probability of drawing a queen followed by a king, we can break down the problem into two parts:
1. The probability of drawing a queen as the first card.
2. The probability of drawing a king as the second card, given that a queen was drawn as the first card.
Let's find each probability step by step:
1. The probability of drawing a queen as the first card:
In a standard deck of 52 cards, there are 4 queens (one of each suit), so the probability of drawing a queen as the first card is 4/52, which can be simplified to 1/13.
2. The probability of drawing a king as the second card, given that a queen was drawn as the first card:
After drawing the queen as the first card, there are 51 cards left in the deck. Out of these, there are 4 kings remaining. Therefore, the probability of drawing a king as the second card is 4/51.
To find the combined probability of drawing a queen followed by a king, we multiply the probabilities of each event:
(1/13) * (4/51) = 4/663
Therefore, the probability of drawing a queen followed by a king, without replacement, is 4/663.