5 5 pt each A security door is unlocked by correctly enterin

5. (5 pt. each) A security door is unlocked by correctly entering 5-digit numeric code. What Is the probability that someone guesses the correct entry code if: (a) digits can be repeated? (b) digits cannot be repeated?

Solution

a)

total number of possibilities

= 10 *10 * 10 * 10 * 10 = 100000

required probability = 1/10000 = 0.00001

b)

total number of possibilities = 10 * 9 *8 * 7 * 6

= 30240
required probability = 1/ 30240 = 0.00003307