If ϕ is an impossible event, then P(ϕ) =

The probability that a new car will get aaward for its design is 0.25, the probability that it will get an award for efficient use of fuel is 0.35 and the probability that it will get both the awards is 0.15. Find the probability that

(i) it will get atleast one of the two awards

(ii) it will get only one of the awards.

The probability that A, B and C can solve a problem are and respectively. The probability of the problem being solved by A and B is , B and C is , A and C is . The probability of the problem being solved by all the three is . Find the probability that the problem can be solved by atleast one of them.

If S is the sample space of a random experiment, then P(S) =

If p is the probability of an event A, then p satisfies