Question

In an after school program, students must choose to either play on the playground or read a book silently. On one cloudy day, 70% of the students chose to play on the playground, and the rest chose read a book silently. 60% of the students who went to the playground are boys, and 20% who stayed inside to read a book are boys. If a student is randomly selected on this day, what is the probability that the student is a girl?

A) 0.46
B) 0.48
C) 0.50
D) 0.52

Answer 1

@ganeshie8 @Rushwr

Answer 2

What did u get ?

Answer 3

@CrazyCountryGirl

Answer 4

Girls who went to the playground are 40% of the student who went to the playground so
probability of selecting a girl from the playground is \[\frac{ 70 }{ 100} * \frac{ 40 }{ 100 } = 0.28\]
Girls who went read a book are 80% from the total of the students who reads books.
So the probability to choose a girls from the reading section is \[\frac{ 30 }{ 100} * \frac{ 80 }{ 100 }\]
that is 0.24
We are asked to find the total probability so we have to add those 2 up ! 0.24 + 0.28 =0.52

Answer 5

Same process of rushwr can be shown with following notation,
\[P[G|Gr] = 0.4\\ P[G|B] =0.8\]
\[P[B] = 0.3 \\P[Gr] = 0.7\]
\[P[G] = P[G\cap Gr] + P[G \cap B]= P[G|Gr]\times P[Gr] + P[G|B]+P[B]\]

G= Girls, Gr = in ground , B = book reading