Question

In a group of 200 students 40 are taking English, 50 are taking math, 12 are taking both. (a) if a student is selected at random, what is the probability that the student is taking English? (b) a student is selected at random from those taking math. What is the probability that the student is taking English? (c) a student is selected at random from those taking English, what is the probability that the student is taking math?

Answer 1

i) 40/200=0.2

ii) 150/200=0.75

iii) 160/200= 0.8

Answer 2

Step-by-step explanation:

The question is of conditional probability .

p(A) = 40/200

p(B) = 50/200

p(A intersection B ) = 12/200

i)P(A) = 0.2

ii) in second question there is asked directly that students are being selected from those taking math ( it has been done ) we have to find probability that student is taking english ( to be finded ).

formula :

p(A|B) = p(A intersection B)/ p(B)

sol :

p(A|B) =

$\frac{12}{200} \times \frac{200}{50}$

(multiplication rule)

=

$\frac{12}{40}$

=0.24

iii) third is also the same its like

p(B|A) = p(A intersection B) / p(B)

( solve by yourself)

= 0.3