Question

A standard deck of 52 cards, has had all its face cards removed so that only the ace through ten ofeach suit remains. A game is played in which two cards are drawn without replacement from this deck and a die is rolled. For the purpose of this game, an ace is considered to have a value of oneFind the probability that the sum of the cards and the die is seven

Answer 1

Given:

A standard deck of 52 cards, has had all its face cards 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 die is rolled. For the purpose of this game, an ace is considered to have a value of one.

Required:

To find the probability that the sum of the cards and the die is seven.

Step-by-step explanation:

he sum of the cards and die is 7.

We have the same number of ways when the 2 cards are different (there is one roll that then adds to 7) and the same number of ways when the 2 cards are the same (once again, there is one roll that adds to 7.

If 2 cards are different, there are

`C(4,1)* C(4,1)=16ways`

If 2 cards are the same, there are

`C(4,2)=6`

Note that the sum of the two cards must be less than 7, as the die is at least 1.

Different:(1,2), (1,3), (1,4),(1,5),(2,3),(2,4) Rolls are then 4, 3, 2, 1, 2, 1

The same: (1,1), (2,2), (3,3) - the roll is then 5, 3, and 1

`\begin{gathered} =6*16+3*6 \\ =114 \end{gathered}`
`\begin{gathered} =(114)/(4680) \\ \\ =(19)/(780) \end{gathered}`

Final Answer:

19/780