Deck of Card Values

563 Words3 Pages
3-1: Consider the experiment of drawing two cards from a deck in which all picture cards have been removed and adding their values (with ace = 1). | | | | A) | Describe the outcomes of this experiment. List the elements of the sample space. | Smallest sum is 2, this happens if both cards are Aces | Largest sum is 20, this happens if both cards are 10s | The other outcomes are integers between the smallest & largest sum (2 and 20) | | | | | | | B) | What is the probability of obtaining a total of 5 for the two cards? | The following results produce a sum of 5: | Ace+4 | | | 2+3 | | | 3+2 | | | 4+1 | | | 4 suits, 4 outcomes equals 16 different ways to get a sum of 5 | As there are 4 suites, this means these 4 combinations could happen in 4 different ways | 16+16+16+16 = 64 | | | | | This is a reduced deck with only 40 cards | Because the first card picked will be any available cards, it equals 40 | The second card picked will be any of the available cards left, it equals 39 | 40 x 39 = 1560 different ways the 19 outcomes | 64 / 1560 = a probability of 0.410 | | | | C) | Let a be the event “total card value is 5 or less.” Find P ( A ) and P ( A c ). | Total card value must equal 2,3,4,5 | As defined in B) there are 64 ways to obtain a sum of 5 | Now must determine how many ways to get a sum of 2, 3, or 4 | 2) | Draw Ace twice in a row, total of 12 ways to obtain sum of 2 | 3) | Draw Ace+2, or 2+Ace. Four Aces and Four Twos. 4x4 = 16 with an Ace selected first. As well as 4x4=16 with a Two selected first. 16+16 = 32 ways to obtain a sum of 3 | 4) | Draw Ace + 3 or 2+2 or 3+Ace. | | | Ace+3 selection, 4x4 = 16 ways to obtain sum of 4 | | | 2+2 select, 4x3 = 12 ways to obtain sum of 4 | | | 3+Ace selection, 4x4 = 16 ways to obtain sum of 4 | | 16+12+16 =

More about Deck of Card Values

Open Document