Final answer:
The probability of selecting a four and then a jack from a well-shuffled 52-card deck is calculated by multiplying the individual probabilities of drawing each card in sequence, without replacement. The final probability is 1/166.
Step-by-step explanation:
To answer how one can find the probability of selecting a four and a jack from a deck of cards, we must first consider the composition of the deck. A standard deck of 52 cards is divided into four suits: clubs, diamonds, hearts, and spades. Each suit contains 13 cards, specifically 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), and K (king). With this understanding, let's calculate the probability in question.
Step 1: Since there are 4 fours and 4 jacks in a deck, the total number of ways to select a four is 4, and the total number of ways to select a jack is also 4.
Step 2: Since the cards are drawn in succession without replacement, after selecting four, we are left with 51 cards in the deck. Therefore, the probability of drawing a jack after a four has been drawn is 4/51.
Step 3: We multiply these probabilities to find the combined probability of both events happening one after the other, which is 4/52 * 4/51.
Step 4: Simplifying this expression gives us 16/2652, which can further be reduced to 1/166. This is the probability of selecting a four and then a jack from a standard deck of 52 cards.
Remember, the sequence here does matter; if the question was about selecting one four and one jack in any order, the calculation would change as it would be a combination problem instead of a permutation problem.