# Sum Probability

## Solution

Anna has Card 7.

Daisy has Card 3.

Jeff has Card 11.

Russ has Card 4.

## Explanation

### Step 1

Find out how many combinations there are for each card.

Make a list.

3 | 4 | 7 | 11 | |
---|---|---|---|---|

Possible combinations | 1 + 2 2 + 1 |
1 + 3 3 + 1 2 + 2 |
3 + 4 4 + 3 5 + 2 2 + 5 1 + 6 6 + 1 |
5 + 6 6 + 5 |

Total number of combinations | 2 | 3 | 6 | 2 |

### Step 2

Find out the total number of possible outcomes using 2 cubes.

6 x 6 = 36

There are 36 possible combinations.

### Step 3

Find out the probability of getting each one of the numbers on the cards.

Use a ratio to find each probability.

combinations possible for each card = |
outcomes in event |

36 | possible outcomes |

3 | 4 | 7 | 11 | |
---|---|---|---|---|

Probability |

### Step 4

Use the clues.

- Anna has the greatest probability of scoring a point on her first turn. She must have Card 7 because it has the probability of 6 out of 36.
- Jeff's and Daisy's cards have the same probability. They must have Cards 3 and 11 because the probability of scoring a point with those cards is 2 out of 36.
- Jeff's card has a higher number than Daisy's. He must have Card 11.
- The probability of Russ earning a point is greater than that of Jeff earning a point. He must have Card 4 because the probability of that card is 3 out of 36.

### Summary

Anna has Card 7.

Daisy has Card 3.

Jeff has Card 11.

Russ has Card 4.