If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting one queen and three kings. The probability is ◻. (Round to six decimal places as needed.)

Question

Bytelearn · Accepted Answer

Calculate Queen Ways: First, let's find out how many ways we can pick one queen out of the four available in the deck. There are 4 queens in a deck, so there are 4 ways to pick one queen. Calculation: 4C1 = 4Calculate King Ways: Next, we need to figure out how many ways we can pick three kings out of the four available in the deck. There are 4 kings in a deck, so there are 4 ways to pick three kings. Calculation: 4C3 = 4Calculate Total Ways: Now, we need to calculate the total number of ways to pick any 4 cards out of 52. Calculation: 52C4 = (52*51*50*49)/(4*3*2*1)Calculate Probability: Let's calculate the probability of getting one queen and three kings. Probability = (Ways to pick one queen * Ways to pick three kings) / Total ways to pick 4 cards Calculation: Probability = (4 * 4) / (52C4)Perform Math Calculation: Now, we do the actual math. Calculation: Probability = (4 * 4) / ((52*51*50*49)/(4*3*2*1))Simplify Calculation: Simplify the calculation. Calculation: Probability = (16) / (270725)Convert to Decimal: Finally, we convert this to a decimal to get the probability. Calculation: Probability = 16 / 270725 ≈ 0.000059

If you are dealt $4$ cards from a shuffled deck of $52$ cards, find the probability of getting one queen and three kings. $\newline$ The probability is $\square$ . $\newline$ (Round to six decimal places as needed.)

Full solution

More problems from Percent of a number: tax, discount, and more

Related topics

If you are dealt 444 cards from a shuffled deck of 525252 cards, find the probability of getting one queen and three kings.\newlineThe probability is □\square□ .\newline(Round to six decimal places as needed.)

If you are dealt $4$ cards from a shuffled deck of $52$ cards, find the probability of getting one queen and three kings. $\newline$ The probability is $\square$ . $\newline$ (Round to six decimal places as needed.)