Answer :

Let p denote the probability of getting 3, 4 or 5 in a throw of dice.


Let us find out the value of p.


We know, a dice has 6 faces numbered 1, 2, 3, 4, 5 and 6.


So, the probability of getting a 3, 4 or 5 is given as,




If p denotes the probability of getting success, then let q denote the probability of not getting success.


We can say,


p + q = 1


q = 1 – p




Let X denote the number of successes in the throw of five dice simultaneously.


Let there be total n number of throws of five dice simultaneously.


Then, the probability of getting r successes out of n throws of dice is given by,


P (X = r) = nCrprqn-r


Now, substitute the value of p and q in the above equation.


Also, put n = 5 (Since there are 5 dice throw)



Now, the probability of getting at least 3 successes is given by


Probability of getting at least 3 successes = P(X = 3) + P(X = 4) + P(X = 5)


Thus,










Thus, the probability of getting 3 successes is 1/2.


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