Question

A box contains 11 two-inch screws, of which 4 have a Phillips head and 7 have a regular head. Suppose that you select 3 screws randomly from the box with replacement. Find the probability there will be more than one Phillips head screw.

Answer 1

The probability that there will be more than one Phillips head screw = 0.1803 .

Explanation:

We are given that there are 11 two-inch screws in a box of which 4 have a Phillips head and 7 have a regular head.

We are selecting 3 screws randomly from the box with replacement, so the probability that there will be more than one Phillips head screw is given by :

• Probability of selecting two Phillips head screw.

• Probability of selecting three Phillips head screw.

Now P(selecting 2 Phillips head screw with replacement) is given by :

Selecting 2 Phillip head screw =
`(4)/(11)` *
`(4)/(11)` =
`(16)/(121)`

P(selecting three Phillips head screw) =
`(4)/(11)` *
`(4)/(11)` *
`(4)/(11)` =
`(64)/(1331)`

Therefore, Probability that there will be more than one Phillips head screw

=
`(16)/(121)` +
`(64)/(1331)` =
`(240)/(1331)` = 0.1803 .