A toolbox contains 3 sizes of Robertson screwdrivers, 4 sizes of Phillips screwdrivers, and 5 sizes of flat-head screwdrivers. If you randomly pull a screwdriver:
a) What are the odds in favor of it being a Robertson screwdriver? Express as reduced ratio.
b) What are the odds against it being a flat- head screwdriver? Express as reduced ratio.
c) What are the odds in favor of it being either a Robertson or a Phillips screwdriver? Express as reduced ratio.
a) Odds in favor of it being a Robertson screwdriver:
There are 3 sizes of Robertson screwdrivers out of a total of 12 screwdrivers in the toolbox.
Odds in favor = Number of favorable outcomes / Number of unfavorable outcomes
Odds in favor = 3 / (12 - 3)
Odds in favor = 3 / 9
Odds in favor = 1 / 3
The odds in favor of it being a Robertson screwdriver are 1:3.
b) Odds against it being a flat-head screwdriver:
There are 5 sizes of flat-head screwdrivers out of a total of 12 screwdrivers in the toolbox.
Odds against = Number of unfavorable outcomes / Number of favorable outcomes
Odds against = 5 / (12 - 5)
Odds against = 5 / 7
The odds against it being a flat-head screwdriver are 5:7.
c) Odds in favor of it being either a Robertson or a Phillips screwdriver:
There are 3 sizes of Robertson screwdrivers and 4 sizes of Phillips screwdrivers out of a total of 12 screwdrivers in the toolbox.
Odds in favor = Number of favorable outcomes / Number of unfavorable outcomes
Odds in favor = (3 + 4) / (12 - 7)
Odds in favor = 7 / 5
The odds in favor of it being either a Robertson or a Phillips screwdriver are 7:5.