60 paintings. T= Painting from 20th century. B= British painting. A painting is chosen random. it is from the 20 century. Work out the probability it is British

The probability will be "0.20".

According to the question,

then,

Therefore,

→

Thus the answer above is right.                                                  

Learn more:

link

P(B | T)=3/13

Step-by-step explanation:

The question is missing the Venn diagram that shows the value of each variable.  

From the Venn diagram we can see there are 10 paintings that not T and not B.  That means the total number of paintings that either T or B is

P(T∪B) = 60-10= 50 paintings.

There are x(x-2) + x paintings from 20th century

P(T)= x(x-2) + x = x^2 - x

There are 2x+8 +x  British paintings.

P(B)= 2x+8 +x  = 3x +8

There are 2 paintings that both T and B

P(T∩B)= x

Using union equation we can find the x

P(T∪B) = P(T) + P(B) - P(T∩B)

50=  x^2 - x + 3x +8 - x

x^2 + x + 8 - 50 = 0

x^2 + x + -42 =0

(x-6) (x+7)=0

x1= 6   x2=-7

Since x can't be minus, then x=6.

The question asking how much conditional probability that a random T paintings is also British. The calculation will be:

P(B|T)= P(B∩T) / P(B) = x/ (3x +8)= 6/(6*3+8)= 6/26= 3/13

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50