Total number of outcomes=6*6=36 Product of the number appear in the dice face is perfect square is ={(1,1)(2,2),(3,3)(4,4)(5,5),(6,6)(4,1)(1,4)}=8 Probability of getting Product of the number appear in the dice face is perfect square is =8/36=2/9
Q2 Three fair dice are thrown.The probability that all three dice have the same number on the face shows up.
Total number of outcomes=6*6*6=216 All three dice have the same number={(1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6)}=6 Probability of all three dice have the same number=6/216=1/36
Q3.A fair dice is tossed two times.The probability that the second toss result in value that is higher than first toss.
Total number of outcomes=36 Second toss result higher than first toss={(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)(5,6)}=15 Probability of Second toss result higher than first toss=15/36=5/12
Q4. A single dice is thrown twice .What is the probability that sum is neither 8 or nor 9.
Total number of outcomes=6*6=36 Dice number Sum is either 8={(4,4),(2,6),(6,2),(3,5),(5,3)}=5 Probability of dice number Sum is either 8=5/36 Dice number Sum is either 9={(5,4),(3,6),(6,3),(4,5)}=4 Probability of dice number Sum is either 9=4/36 Probability of getting dice number Sum is neither 8 or nor 9=1-(5/36)-(4/36)=27/36 =3/4
Q5.A fair dice is rolled twice.The probability that an odd number follow an even number is
Total number of outcomes=36 When dice rolled twice odd number follow an even number is={(2,1),(4,1),(6,1),(2,3),(4,3),(6,3),(2,5),(4,5),(6,5)}=9 Probability of When dice rolled twice odd number follow an even number is=9/36=1/4
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