Question

6. A monkey hits the keys of a typewriter at random, picking each of the 26 letters of the English alphabet each time, regardless of what it has picked before. What is the probability that the first 6 letters that it types form the word ORANGE, by rearrangement, if necessary? 7. A standard deck of 52 cards is shuffled, and three cards are dealt one by one. What is the probability of the first card being a spade and the second being a heart and the third being a diamond.

Answer 1

6. Since ORANGE has all 6 different letters and we don't want the exact same formation, we just need the monkey to choose these 6 letters. So the probability of this is : 6/26C6 = 2.6061*10^-5

7. There are 13 cards of spade, heart, diamond in a standard deck of 52 cards.

So probability that the first is a spade= 13/52

Probability that the second is a heart = 13/51

Probability that the third is a diamond = 13/50

So required probability = 13*13*13/52*51*50 = 0.01657