Question

Emily and Jennifer are playing a game with dice. Each one has a die. If each one rolls one and the sum of the numbers are 7 or 11 they win. If the sum is 2, 3 or 12 they lose. If it is any other number there is no winner or loser.

Find the sample space by either creating a tree or a chart/table. (remember, each die has the numbers 1-6 on it).
Then find:
P (they win - if the sum is 7 or 11)
P (they lose - if the sum is 2, 3 or 12)
The total sample space. HINT: How many total possible combinations?

wrong answers and links will be reported. /srs

Answer 1

For 7 or 11

• S={(1,6),(2,5),(5,2),(6,1),(3,4),(4,3),(6,5),(5,6)}

For 2,3 and 12

• S={(1,1),(1,2),(2,1),(6,6)}

Total:-

8 elements in sample space

Answer 2

**Please see attached for the sample space**

• The winning combinations are highlighted in green.
• The losing combinations are highlighted in red.

From inspection of the sample space:

• Total number of ways the sum is 7 or 11 (win) = 8
• Total number of ways the sum is 2, 3 or 12 (lose) = 4
• Total number of possible outcomes = 36

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

`\sf \implies P(win)= (8)/(36)=\frac29`

`\sf \implies P(lose)= (4)/(36)=\frac19`