Art of problem solving An urn contains 10 balls numbered from 1 to 10. Carlo and Eric each draw a ball at the same time. Given that Carlo's number was higher than Eric's, what is the probability that Carlo drew a 6?

11.11% probability that Carlo drew a 6

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible results:

(Carlo, Eric)

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1), (7,1), (8,1), (9,1),(10,1)

(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2), (8,2), (9,2),(10,2)

(1,3), (2,3), (3,3), (4,3), (5,3), (6,3), (7,3), (8,3), (9,3),(10,3)

(1,4), (2,4), (3,4), (4,4), (5,4), (6,4), (7,4), (8,4), (9,4),(10,4)

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5), (7,5), (8,5), (9,5),(10,5)

(1,6), (2,6), (3,6), (4,6), (5,6), (6,6), (7,6), (8,6), (9,6),(10,6)

(1,7), (2,7), (3,7), (4,7), (5,7), (6,7), (7,7), (8,7), (9,7),(10,7)

(1,8), (2,8), (3,8), (4,8), (5,8), (6,8), (7,8), (8,8), (9,8),(10,8)

(1,9), (2,9), (3,9), (4,9, (5,9), (6,9), (7,9), (8,9), (9,9),(10,9)

(1,10), (2,10), (3,10), (4,10), (5,10), (6,10), (7,10), (8,10), (9,10),(10,10)

Desired outcomes:

Carlo drawing a six, higer than Eric

(6,1),(6,2),(6,3),(6,4),(6,5)

5 possible outcomes

So D = 5.

Total outcomes:

Given that Carlo's number was higher than Eric's, so only pairs in which Carlo is higher than Eric

(2,1), (3,1), (4,1), (5,1), (6,1), (7,1), (8,1), (9,1),(10,1)

(3,2), (4,2), (5,2), (6,2), (7,2), (8,2), (9,2),(10,2)

(4,3), (5,3), (6,3), (7,3), (8,3), (9,3),(10,3)

(5,4), (6,4), (7,4), (8,4), (9,4),(10,4)

(6,5), (7,5), (8,5), (9,5),(10,5)

(7,6), (8,6), (9,6),(10,6)

(8,7), (9,7),(10,7)

(9,8), (10,8)

(10,9)

45 total outcomes

So T = 45

Probability

11.11% probability that Carlo drew a 6

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour