Question

The sample space of picking a 2

character password using the letters Y, P, GR,
B, O, where double letters are not allowed is
shown. Your teacher asks the class to find the
probability of choosing a password with
one Y and one P. Carlos incorrectly says that
the probability is 15. Find the correct probability
then decide which error Carlos might have
made

Answer 1

`Pr = (1)/(15)`

Explanation:

Given

See attachment for sample space

Required

`P(1\ Y\ and\ 1\ P)`

From the attached sample space, we have:

`n(S) =30` ---- total outcomes

`n(PY) = 2` --- outcomes with 1 Y and 1 P = 2 i.e. (P,Y) and (Y,P)

So, the required probability is:

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

`Pr = (2)/(30)`

`Pr = (1)/(15)`

The error is that; Carlos omitted the numerator