A deck of playing cards has four suits, with thirteen cards in each suit consisting of the numbers 2 through 10, a jack, a queen
, a king, and an ace. The four suits are hearts, diamonds, spades, and clubs. A hand of five cards will be chosen at random. Which statements are true? Check all that apply.
The total possible outcomes can be found using 52C5.
The total possible outcomes can be found using 52P5.
The probability of choosing two diamonds and three hearts is 0.089.
The probability of choosing five spades is roughly 0.05
The probability of choosing five clubs is roughly 0.0005.
Since order does not matter, you use a combination and not a permutation, so the first one is true, which means the second one is not true. The probability of choosing two diamonds and three hearts can be represented by (13C2 * 13C3)/52C5, which is 0.0086, not 0.089, so the third one is not true. The probability of choosing five spades and the probability of choosing five clubs are represented by the same thing, 13C5/52C5, which is roughly 0.0005, so the fourth one is not true but the fifth one is. So the answer is the first and fifth one.
