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:

Question

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.

Answer 1

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.