Question

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c, respectively. Of these subjects the student has 75% chance of passing in atleast one, a 50% chance of passing in atleast two and a 40% chance of passing in exactly, two, which of the following relations are true.

(a) p+ m +c= 27/20
(b) p+ m +c= 13/20
(c) pmc= 1/10
(d) Both (a) and (c)

Please provide step wise explanation​

Answer 1

Option B is correct plz mark me brilliant

Answer 2

Both (a) p + m + c = $\frac{27}{20}$ and (c) pmc = $\frac{1}{10}$ are true.

Step-by-step explanation:

Let s, t, u, v, w, x, y and z are the probabilities of the respective regions.

Thus, we have:

s + t + u + v + w + x + y = 0.75     ...(i)  

v + w + x + y = 0.5     ...(ii)  

v + w + x  = 0.4     ...(iii)  

Thus, subtracting (ii) and (iii): y = pmc = 0.1 = $\frac{1}{10}$

Here, y refers to the intersection of all the three and hence equals p.c.m since they are independent events.

Again, subtracting (i) and (ii): s + t + u = 0.25

We need to find m + c + p:

m + c + p = s + t + u + 2(v + x + x) + 3y

               = 0.25 + 2 x 0.4 + 3 x 0.1

               = 1.35

               = $\frac{27}{20}$

Hence, option (d) is correct.