Two cards are drawn at random froma standard deck of 52 cards without replacement. What is the probability if drawing a 7 and a king in that order?
prob of 7 = 4/52
leaving 51 cards, so prob a king = 4/51
prob(your event) = (4/52)(4/51) = 4/663
To calculate the probability of drawing a 7 and a king in that order from a standard deck of 52 cards without replacement, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's find the number of favorable outcomes. There are 4 kings in a deck, and once we draw one, there will be only 3 kings left. Similarly, there are 4 sevens, and once we draw one, there will be only 3 sevens left. Since we want to draw a 7 and then a king, the number of favorable outcomes is 4 (kings) multiplied by 4 (sevens) = 16.
Next, let's calculate the total number of possible outcomes. In this scenario, we are drawing two cards without replacement, so for the first card, there are 52 possibilities. Then, for the second card, there will be 51 cards remaining. Therefore, the total number of possible outcomes is 52 multiplied by 51 = 2,652.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: 16 divided by 2,652.
Therefore, the probability of drawing a 7 and a king in that order from a standard deck of 52 cards without replacement is approximately 0.006 or 0.6%.