Slide 1 : Notations:
Let A and B by two events, then
(i) A' or or Ac stands for the non-occurrence of negation of A.
(ii) AUB stands for the occurrence of at least one of A or B.
(iii) A ? B stands for the simultaneous occurrence of A and B.
(iv) A' ? B' stands for the non-occurrence of both A and B.
(v) A ? B stands for "the occurrence of A implies occurrence of B". Reliance Maths Academy Parbhani
Illustration: : Illustration: A die is rolled. What is the probability that outcome will be an even number? Reliance Maths Academy Parbhani
Slide 3 : Two dice are thrown simultaneously. What is the probability of obtaining a total score of seven? Reliance Maths Academy Parbhani
Slide 4 : Reliance Maths Academy Parbhani Suppose a die is rolled, can we find the probability that either odd
number or a number divisible by 4 comes?
Slide 5 : Now, think about a different situation: A die is rolled, can we calculate the probability that the number, which comes is either odd or divisible by 3?
Slide 6 : Reliance Maths Academy Parbhani Note:
1. In previous case, P(AUB) = P(A) + P(B) was correct because AnB = ?. So, we get a very important result.
P(AUB) = P(A) + P(B) when A and B are mutually exclusive events.
P(AUB) = P(A) + P(B) - P(AnB), when A and B are not mutually exclusive events.
2. This particular case of two events can easily be generalized for the three events A, B and C
P(AUBUC) = P(A) + P(B) + P(C) - P(AnB) -
P(BnC) - P(CnA) + P(AnBnC).
Slide 7 : From a bag containing 5 white, 7 red and 4
black balls a man draws 3 balls at random.
Find the probability that all are white. Reliance Maths Academy Parbhani
Slide 8 : In a, science course 20% took Higher Mathematics, 50% took Physics and 5% took both Higher Mathematics and Physics. A candidate is chosen at random. The probability that the chosen candidate took neither Higher Mathematics nor Physics is,
(a) (b)
(c) (d)
Slide 9 : Three integers are chosen at random from the first 20
integers. The probability that their product is even is :
(a)
(b)
(c)
(d)
Slide 10 : Three six faced dice are tossed together. The
probability that exactly two of the three numbers are
equal is
(a)
(b)
(c)
(d) None of these
Slide 11 : The probability for a randomly chosen month to have
its 10th day as Sunday is :
(a)
(b)
(c)
(d)
Slide 12 : Thank You