To get home, Renae can take one of four buses: #41. #28. #55, or #81. Once she is on a bus, she will randomly select one of the
following equally likely activities: listening to her music player, writing a letter, or reading a book. Her choice of bus and choice of entertainment are independen
events, because the bus that Renae took did not affect which activity she chose. For example, what is the probability that Renae writes a letter if she takes the
#41 bus? What is the probability that Renae writes a letter if she takes the #55 bus?

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-12-20T12:39:52+01:00

The probability that Renae writes a letter if she takes the #55 bus is 1/12

The buses are given as:

Buses: #41, #28, #55, #81

There are 4 buses of equal probabilities.

So, the probability that she takes the #55 is:

[tex]P(55)= \frac 14[/tex]

The activities are given as:

Activities: listening to her music player, writing a letter, or reading a book

There are 3 activities of equal probabilities.

So, the probability that she writes a letter is:

[tex]P(Letter)= \frac 13[/tex]

The probability that she does both independent events is:

[tex]Pr = P(55) \times P(Letter)[/tex]

So, we have:

[tex]Pr = \frac 14 \times \frac 13[/tex]

[tex]Pr = \frac 1{12}[/tex]

Hence, the probability is 1/12