Two-integers-x-and-y-are-chosen-with-replacement-out-of-the-set-0-1-2-3-10-Then-the-probability-that-x-y-gt-5-is-

Question Number 26851 by jain50791@gmail.com last updated on 30/Dec/17

Two integers x and y are chosen with

replacement out of the set {0, 1, 2, 3, \dots, 10} .

Then the probability that ∣ x - y ∣> 5 is

Commented by Rasheed.Sindhi last updated on 30/Dec/17

Let x > y

∣ x - y ∣> 5 \Rightarrow x - y > 5 \Rightarrow x > y + 5

y = 0 \Rightarrow x = 6, 7, \dots, 10 (5 values)

[5 Satisfying pairs]

y = 1 \Rightarrow x = 7, 8, \dots, 10 (4 values)

y = 2 \Rightarrow x = 8, \dots, 10 (3 values)

y = 3 \Rightarrow x = 9, 10 (2 values)

y = 4 \Rightarrow x = 10 (1 values)

Total satifying pairs : 15 for x > y

∵ (a, b) satisfy \Rightarrow (b, a) also satisfy

Total satifying pairs : 15 for x < y

[Note that for x = y no pair satisfy]

Hence number of all pairs which

satisfy ∣ x - y ∣> 5 is 15 + 15 = 30

Number of all possible pairs of the

domain set

= 11 \times 11 = 121

Probability = \frac{Number of satisfying pairs}{Number of total pairs}

Probability = \frac{30}{121}