Answer:
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
Step-by-step 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)
[tex] P(6)= (\frac{1}{4})(\frac{2}{3}) +(\frac{2}{4})(\frac{1}{3})[/tex]
[tex] P(6) =\frac{2}{12} + \frac{1}{6} = \frac{1}{3} [/tex]
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)
[tex] P(7)= (\frac{1}{4})(\frac{1}{3}) +(\frac{1}{4})(\frac{1}{3})[/tex]
[tex] P(7) =\frac{1}{12} + \frac{1}{12} = \frac{1}{6} [/tex]
If the sum is a 8: (4+4)
[tex] P(8)= (\frac{2}{4})(\frac{1}{3})=\frac{1}{6}[/tex]
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)
[tex] P(9)= (\frac{2}{4})(\frac{1}{3}) +(\frac{1}{4})(\frac{2}{3})[/tex]
[tex] P(9) =\frac{1}{6} + \frac{1}{6} = \frac{1}{3} [/tex]
[tex] P(6) = \frac{1}{3} [/tex]
[tex] P(7) = \frac{1}{6} ;P(8) = \frac{1}{6} [/tex]
[tex]P(7) or P(8) = \frac{1}{6} + \frac{1}{6} = \frac{1}{3} [/tex]
[tex] P(9) = \frac{1}{3} [/tex]
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
