In the final exams, 40% of the students failed chemistry, 25% failed physics, and 19% failed both chemistry and physics. What is the probability that a randomly selected student failed physics given that he passed chemistry? I have answered the question in the image below, but I would like to know if it is correct. If it is not, please include an explanation of why, as well as the step by step to get the correct answer

I did a similar question for my homework, you can check mine.

Step-by-step explanation:

In an examination 30% of the students failed in Physics, 25% in Mathematics and 12% in both Physics and Mathematics. A student is selected at random. Find the probability that the student has failed in Physics, if it is known that he has failed in Mathematics. (ii) the student has failed at least one of the two subjects (ii) the student has passed at least one of the two subjects (iv) the student has passed in Mathematics if he failed in Physics.

Ans:

let the event of student failed in physics be P

let the event of student failed in maths be M

P(P) = 3/10

P(M)= 1/4

P(P nn M) =3/25

(I)

P(P/M)= (P(P nn M))/(P(M)) = (3/25)/(1/4) = 12/25

(ii)

P(P uu M) = P(P) + P(M) -P(P nn M)

= 3/10 + 1/4 - 3/25 = 43/100 = 0.43

(iii)

P=1 - P(P nn M) = 1 - 12/100 = 88/100 =22/25

(iv)

p-> 30 , m-> 25

P nn M -> 12

P= 18/30 = 3/5

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3