Problem Solving

Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.
The answer is No, cud u let me know how?

2) The probability that a student will pass the final examination in both English and Maths is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Maths examination?

2) The probability that a student will pass the final examination in both English and Maths is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Maths examination?

P(E)+P(M)-P(E&M)+P(notE&notM)=1
0,75+x-0,5+0,1=1
x=0,65

passing english exam is independent of passing the math exam,isnt it ?
so p(a and b) = p(a) * p(b)
applying that answer is 2/3.
0.1 value seems to be redundant.
some please confirm ?

sorry i confirm 4meonly is correct.maybe i confused myself..
probability of passing neither is 0.1
which means probability of passing either english or math = 0.9
p (a or b) = p(a) +p(b) -p(a and b) ..basic rule
0.9 = 0.75+p(m) -0.5
p(m) =0.65

thanks, yes the answer is 0.65

Cud someone help understand the first question as well of mutually exclusive events.

P(not E or not F) if were mutually exclusive then it is true that

P(not E)+ P(not F) = 0.25

1-P(E) + 1-P(F) = 0.25

2-0.25 = P(E) + P(F) (exclusive E & F) events. comes out to be greater than 1 . Probability can't be greater than 1 so it s not exclusive. There has to be some intersection between those two events.

thanks