Consider the experiment of drawing two cards from a deck in

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). Let A be the event \"total card value is 5 or less.\" Find P(A) and P(A{compliment}

Solution

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).   |
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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) |
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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 | |
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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 |
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C) | Let a be the event