What is the probability?

Question

Jari draws 4 cards at random from a regular deck of cards without replay. What is the probability that he gets

a) Spades

b) at least 1 king

Answer 1

There are 52 cards in a standard deck. Jari draws 4 cards without replacement.

a) There are 13 spades in the standard deck. Jari draws 4 cards with spades in no particular order.

C(13, 4) = 13! / (4!)(9!) = 78 ways to draw 4 cards with spades.

P(4 spades) = C(13, 4) / C(52, 4) = 78 / 270,725 = 2.881× 10^-4 = 0.0002881

The probability that Jari will draw 4 spades is 0.0002881.

b) There are 4 kings in the standard deck. Jari draws 4 cards with at least 1 king in no particular order.

C(4, 1) = 4! / (1!)(3!) = 4 ways to draw a card with a king in any suit.

C(48, 3) = 48! / (3!)(45!) = 17,296 ways to draw 3 cards other than a king in any suit.

P(at least 1 king) = C(4, 1)*C(48, 3) / C(52, 4) = [(4)*(17,296)] / (270,725) = 0.2556

The probability that Jari will draw 4 cards with at least 1 king is 0.2556.

Answer 2

4:48 is the odds for each..................

Answer 3

a) I'm going to assume the question is asking what the probability is of getting ALL FOUR cards as noted.

The first draw, the probability = 13/52 = 1/4

The second draw, the probability = 12/51 = 4/17

The third draw, the probability = 11/50

The fourth draw, the probability = 10/49

The probability that all 4 things happen is the product of the individual probabilities = 1/4•4/17•11/50•10/49 = 11/4165 or 0.00264 or 0.264 %

b) To do the condition with "at least 1 king" it's easier (for me) to consider the probability of getting no kings and then flipping the results. So the probability of getting no king is calculated as follows:

Draw #1: The probability (no king) = 48/52 = 12/13.

Draw #2: The probability (no king) = 47/51.

Draw #3: The probability (no king) = 46/50 = 23/25.

Draw #4: The probability (no king) = 45/49.

The total probability (no king) = 12/13•47/51•23/25•45/49 = 583740/812175 = 38916/54145 = 0.7187 = 71,87%

To switch it to "at least 1 king", since the probability of getting "no kings" or getting "at least 1 king" is 100% (or 1). then the probability of getting at least 1 king = 1 - 38916/54145 = 15229/54145 = 0.2813 = 28.13%