(1) - As pack contains cards numbered 1 to 20, if a card is selected at random, all have equal probability of being selected and probability of each is 120. As such probability of getting 6 is 120. We get a multiple of 3, when we get {3,6,9,12.15.18} and hence probability of getting a multiple of 3 is 620=310. Prime numbers between 1 and 20 are {1,2,3,5,7,11,13,17,19} and hence probability of getting prime numbers is 920. It is apparent from this that probability of not getting a prime is 1120.
(2) As book is page numbered 1 to 45, odd numbers will appear on left hand side and even on right hand side and it could open at 1 or 2-3 or 4-5 and so on and lastly 44-45 - 22 possibilities. 3 will appear when we get 2-3, 12-13, 22-23, 30-31, 32-33, 34-35, 36-37, 38-39 and 43-44 and probability of appearing a page number containing 3 will be 922.
(3) As probability of getting a blue marble is 12 and getting a red marble is 13, the probability of getting a yellow marble is 1−12−13=16
(4) As among red and blue beetles, there is a 75%=34 probability of randomly selecting a red beetle and there are 24 red beetles, we have 100%−75%=25% blue beetles and there number will be 243=8 (as 25% is one-third of 75%) and we have 24+8=32 beetles altogether.
(5) As the cards are numbered 1 to 9 and there are 9 possibilities, getting less than 8 means getting 1 to 7 and probability of Arun getting it is 79. Sally loses if she gets less than 6 on die and as a die contains six faces numbering 1 to 6, probability of Sally loosing is 56 and she has 16 chance of winning. Hence, Arun has greater chance of winning game.
