Question

Rodney packs 3 shirts for a trip. It is early morning so he just grabs 3shirts randomly from his closet. The closet contains 10 shirts: 5 striped, 3 plaid, and 2solid colored ones. What is the probability that he chose 2 striped and 1 plaid shirt

Answer 1

Probability of choosing 2 stripped and 1 plaid shirts = 0.25

Explanation:

Number of stripped shirt in the closet = 5

Number of plaid shirts = 3

Number of solid color shirts = 2

Total number of shirts = 10

Number ways to pick 2 stripped out of 5 stripped shirts =
`^5C_2`

=
`(5!)/(2!(5-2)!)`

= 10

Similarly, number of ways to pick 1 plaid shirt out of 3 plaid shirts =
`^3C_1`

=
`(3!)/(2!(3-2)!)`

= 3

Total number of ways to pick 3 shirts out of 10 =
`^(10)C_3`

=
`(10!)/(3!(10-3)!)`

= 120

Therefore, probability of choosing 2 stripped and 1 plaid shirt

=
`\frac{\text{Favorable outcome}}{\text{Total outcomes}}`

=
`(10* 3)/(120)`

=
`(1)/(4)`

= 0.25