We throw 5 dice What is the probability that at least 2 of t

We throw 5 dice. What is the probability that at least 2 of them has the same value? Instruction: Compute the probability p of the complement event. Then the answer is 1 - p.

Solution

Method 1 :-

Probability of getting a value when a dice is thrown once = p = 1/6

Probability of not getting a value when a dice is thrown once = 1 - p = 1 - 1/6 = 5/6.

The Probability of getting any value k times when thrown n times = (n C k) * (p^k) * (1 - p)(^n-k)

where...

n = 5

k = 2,3,4,5 // since at least 2 which means minimum 2

So the probability of at least two has the same value =

(5 C 2)(1/6)² (5/6)³ + (5 C 3)(1/6)³ (5/6)² + (5 C 4)(1/6)⁴ (5/6)¹ + (5 C 5)(1/6)⁵