The number of exhaustive outcomes is 36. Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2 P(E) = 1 - 1/2 = 1/2.
As we know we have 10 letter and 10 different address and one more information given that exactly 9 letter will at the correct address....so the remaining one letter automatically reach to their correct address P(E) = favorable outcomes /total outcomes Here favorable outcomes are '0'. So probability is '0'.
In a family with 2 children there are four possibilities: 1) the first child is a boy and the second child is a boy (bb) 2) the first child is a boy and the second child is a girl (bg) 3) the first child is a girl and the second child is a boy (gb) 4) the first child is a girl and the second child is a girl (gg)
But already given that one child is boy. So we have three possibilities of (bb)(bg)(gb). n(E)= both are boys=BB=1 n(S)= 3 Required probability P = n(E)/n(S) = 1/3.
In a circle of n different persons, the total number of arrangements possible = (n - 1)! Total number of arrangements = n(S) = (15 – 1)! = 14 ! Taking three persons as a unit, total persons = 13 (in 4 units) Therefore no. of ways for these 13 persons to around the circular table = (13 - 1)! = 12! In any given unit, 3 particular person can sit in 3!. Hence total number of ways that any three person can sit = n(E) = 12! X 3! Therefore P (E) = probability of three persons sitting together = n(E) / n(S) = 12! X 3 ! / 14! = 12!x3x2 / 14x13x12! = 6/14x13 = 3/91