Question

A hat contains four balls. The balls are numbered 2, 4, 4, and 5. One ball is randomly selected

and not replaced, and then a second ball is selected. The numbers on the two balls are added
together.
A fair decision is to be made about which of three sizes of ice cream cone will be ordered, using
the sum of the numbers on the balls. The sizes are small, medium and large.
Which description accurately explains how a fair decision can be made in this situation?


If the sum is 6 or 7 small cone will be ordered. If the sum is 8medium cone will be ordered. If the sum is 9, a large cone will be ordered

If the sum is 6 or 9. a small cone will be ordered If the sum is 7 a medium cone will be ordered If the sum is 8 large cone will be ordered

the sum is 6, a small cone will be ordered . the sum is 7 or 8 , a medium cone will be ordered. If the sum is 9, a large cone will be ordered.

If the sum is 6, a small cone will be ordered . If the sum is 7 or 9, a medium cone will be ordered If the sum is 8 a large cone will be ordered

Answer 1

C) If the sum is 6, a small cone will be ordered . the sum is 7 or 8 , a medium cone will be ordered. If the sum is 9, a large cone will be ordered

Explanation:

If the sum is a 6: (2+4) or (4+2)

P(6) = (2 is first picked)(4 is picked next) + (4 is first picked)(2 is picked next)

`P(6)= ((1)/(4))((2)/(3)) +((2)/(4))((1)/(3))`

`P(6) =(2)/(12) + (1)/(6) = (1)/(3)`

If the sum is a 7: (2+5) or (5+2)

P(7) = (2 is first picked)(5 is picked next) + (5 is first picked)(2 is picked next)

`P(7)= ((1)/(4))((1)/(3)) +((1)/(4))((1)/(3))`

`P(7) =(1)/(12) + (1)/(12) = (1)/(6)`

If the sum is a 8: (4+4)

`P(8)= ((2)/(4))((1)/(3))=(1)/(6)`

If the sum is a 9: (4+5) or (5+4)

P(9) = (4 is first picked)(5 is picked next) + (5 is first picked)(4 is picked next)

`P(9)= ((2)/(4))((1)/(3)) +((1)/(4))((2)/(3))`

`P(9) =(1)/(6) + (1)/(6) = (1)/(3)`

`P(6) = (1)/(3)`

`P(7) = (1)/(6) ;P(8) = (1)/(6)`

`P(7) or P(8) = (1)/(6) + (1)/(6) = (1)/(3)`

`P(9) = (1)/(3)`

Therefore, if the sum is 6, a small cone will be ordered . the sum is 7 or 8 , a medium cone will be ordered. If the sum is 9, a large cone will be ordered