In: Math
a) How many possible numbers can you choose from?
- The range is 000-999. Thus, there are total 1000 possible number to choose (Each digit can be selected in 10 ways and 3 such digits can be selected in 10^3 = 1000 ways)
b) If all 3-digit numbers is equally likely what is the probability of any 1 specific number exactly matches the winning number?
- If all 3-digit numbers are equally likely then, P(1 specific number exactly matches the winning number) = 1/1000 = 0.001
c) Suppose you pick number 156 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?
- If order doesn't matter then these three digits can be arranged in 3! ways = 6 ways
And total events possible are 100
Thus, required probability = 6/1000 = 0.006
d) Suppose you pick the number 111 and you can win if the winning number contains these 3 digits in any order. What is the probability you win?
- Even though it is mentioned order doesn't matter, 111 can be selected only in 1 way
Thus. required probability = 1/1000 = 0.001