Question

Lil' HydroPhil owns five pieces of precious apparel and wants to choose two to wear to the awards show. He defines his precious apparel as: platinum nose ring, diamond shirt, titanium boots, suede pants, and beryllium hat. Assuming the selection is random and each has an equally likely outcome, determine the probability HydroPhil chooses a combination that includes the suede pants.

Answer 1

The probability HydroPhil chooses a combination that includes the suede pants is 0.40

Explanation:

Given

Let

`P \to Platin um\ no se\ ri ng`

`D \to Diamond\ shirt`

`T \to Titanium\ boots`

`S\to Suede\ pants`

`B\to Beryllium\ hat`

Required

Probability of selecting a combination that has S

First, list out all possible combinations (A) of 2

`A = \{PD, PT, PS, PB, DT, DS, DB, TS, TB, SB\}`

The sample size is:

`n(A) = 10`

The combinations that has S are:

`S \to \{PS, DS, TS, SB\}`

The size is:

`n(S) = 4`

So, the probability that he choose the combination that has S is:

`Pr = (n(S))/(n(A))`

`Pr = (4)/(10)`

`Pr = 0.40`