Question

Two bowls are on a teacher's desk. One contains hard candy while the other contains gum. The bowl that contains the hard candy has 10 peppermints, 5 cinnamon disks, and 7 butterscotch. The bowl that contains the gum has 3 bubble gums, 9 Dentine, and 6 spearmints. If you draw one piece from each bowl, find the following probabilities.

P(peppermints, bubblegums)_

P(not butterscotch, Dentine)_

P(cinnamon or butterscotch, spearmint)_

Answer 1

(a)5/66

(b)15/44

(c)2/11

Explanation:

Candy Bowl

Number of Peppermints=10

Number of cinnamon disks=5

Number of butterscotch=7

Total=10+5+7=22

Gum Bowl

Number of bubble gums=3

Number of Dentine=9

Number of spearmints=6

Total=3+9+6=18

(a)P(peppermints, bubblegums)

P(peppermints)
`=(10)/(22)`

P(bubblegums)
`=(3)/(18)`

P(peppermints, bubblegums)
`=(10)/(22)X (3)/(18) =(5)/(66)`

(b)P(not butterscotch, Dentine)

P(butterscotch)
`=(7)/(22)`

P(not butterscotch)
`=1-(7)/(22)=(15)/(22)`

P(Dentine)
`=(9)/(18)`

P(not butterscotch, Dentine)
`=(15)/(22) X (9)/(18)=(15)/(44)`

(c)P(cinnamon or butterscotch, spearmint)

`\text{P(cinnamon)=}(5)/(22) \\\text{P(butterscotch)=}(7)/(22) \\\text{P(cinnamon or butterscotch)=}(5)/(22) +(7)/(22) =(12)/(22) \\\text{P(spearmint)=}(6)/(18) \\\text{P(cinnamon or butterscotch, spearmint)=}(12)/(22) X (6)/(18) =(2)/(11)`