Question

Umbuggio has two microphones which he uses to
teach in RH100; one is
Sony
and one is
Telefunken.
The
Sony
fails with probability .3, while the
Tele-
funken
fails with probability .4. On Monday morn-
ing, Umbuggio picks a microphone at random. What
is the probability that it will fail?
(a) .7
(b) .35
(c) .12
(d) .58
(e) .42
(f) none of the above

Answer 1

And you need to find \(P(pass')\), which is =

\(P(pass'|Sony)P(Sony)+P(pass'|Telefunken)P(Telefunken)\\~\\=\left(.3\right)\left(\dfrac{1}{2}\right)+\left(.4\right)\left(\dfrac{1}{2}\right)\\=\cdots~?\)