Suppose we conduct an experiment and S is the set that contains all of its possi
ID: 3119997 • Letter: S
Question
Suppose we conduct an experiment and S is the set that contains all of its possible outcomes. For example, if the experiment is tossing a six-sided dice1 , then S = {1, 2, 3, 4, 5, 6}. If we repeat the experiment k times, the set of outcomes are the elements in the set S k = S × S × · · · × S, the cross product of k copies of S.
Assume the the dice in the above experiment is not biased so that it is equally likely for a toss to produce any of the six numbers. The probability that when a dice is tossed two times and the first toss produces an even number is simply |A|/|S| ^2 . Similarly, the probability that when a dice is tossed two times and the second toss produces an even number is simply |B|/|S|^ 2 . Compute these two probabilities.
Explanation / Answer
Solution :- As we know that Dice has six faces no such like S = {1, 2, 3, 4, 5, 6}
Among Six Face the Even value faces are Three = {2, 4, 6}
Similarly Among Six Face the Odd value faces also Three = {1, 3, 5,}
(1)Now we have to calculate The probability that when a dice is tossed two times and the first toss produces an even number is simply |A|/|S| 2
First toss probability to have Even Value would be = 3/6
but as required toss is two times so in second toss there is No even faces so its probability would be = 1-(3/6) = 3/6
For our problem Value |A|/|S| 2 would be mutualy happen of above two conditions so Final probability= (3/6) x(3/6 )
= (1/2) x (1/2) |A|/|S| 2 Final probability = 1/4 ANSWER
(2) when a dice is tossed two times and the second toss produces an even number is simply |B|/|S| 2
Similarly as above case |B|/|S| 2 Final probability = (1-3/6)x3/6 = 1/4 ANSWER
Conclution values of |A| , |S| , |B| = 3 , 6 , 3 Respectively
and so |A|/|S|x2 = 3/(6x2) = 1/4 ANSWER
and also |B|/|S|x2 = 3/(6x2) = 1/4 ANSWER