Final answer:
The probability of being dealt a nine and a King from a standard 52-card deck in one draw is 0, but if this refers to drawing two cards without replacement, the probability is 0.006 or 0.6%.
Step-by-step explanation:
The student is asking about the probability of being dealt a nine and a King from a standard 52-card deck in one draw. This cannot happen since you can only draw one card at a time, and a card cannot be a nine and a King simultaneously. Assuming the question refers to drawing two cards one after the other without replacement, the probability would be the product of the probabilities of drawing a nine first and then a King (or vice versa), considering there are four nines and four Kings in the deck.
Here's how to calculate it step by step:
- Calculate the probability of drawing a nine (4 out of 52).
- Calculate the probability of drawing a King next, now with one less card in the deck (4 out of 51).
- Multiply the two probabilities together.
Remember, the events are independent because we're drawing without replacement; the outcome of the first draw affects the outcome of the second. Mathematically, the calculation is as follows:
(4/52) × (4/51) = 16/2652, which simplifies to approximately 0.006 or 0.6% probability.