Nelson Mathematics of Data management 4.6

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" A standard deck of cards has had all face cards ( Jack, Queens, and Kings) removed so that only the ace through ten of each suit remains. A game is played in which two cards are drawn (without replacement) from this deck and a six-sided die is rolled. For the purpose of this game, an ace is considered to have a value of 1."

Question: Find the probability that the sum of the cards and the die is 7

Homework Equations

Doing this for a friend and i don't recall the equations for Permutations and Combinations and probability... Sorry!

The Attempt at a Solution

I was able to get out of a deck of 40 cards the possible number of outcomes are 1560(40x39) and 1/6 since it's a die.
My final answer i got was 1/624
the number of possible out comes in the deck is 15 that have a combination lower than 6.

 

[nate808]

To find the probability that the sum of the cards and the die is 7, we first need to calculate the total number of possible outcomes in the game. Since there are 40 cards in the deck and we are drawing 2 cards without replacement, the total number of possible outcomes is 40*39 = 1560. Additionally, there are 6 possible outcomes for the roll of the die. Therefore, the total number of possible outcomes in the game is 1560*6 = 9360.

Next, we need to determine how many of these outcomes result in a sum of 7. We can do this by listing all the possible combinations of cards and die rolls that result in a sum of 7:

1+6 = 7
2+5 = 7
3+4 = 7
4+3 = 7
5+2 = 7
6+1 = 7

Since there are 6 possible combinations, the probability of getting a sum of 7 is 6/9360 = 1/1560. Therefore, the probability that the sum of the cards and the die is 7 in this game is 1/1560.