Two tiles are randomly chosen one at a time and placed in the order in which they were chosen. Determine the probability that the tiles are:i.COii.Both vowels
PART 1: On the first draw, you have 1 desired outcome (C) out of 7 possible letters. P(first letter is C) = 1/7 On the second draw, you have 1 desired outcome (O) out of *6* remaining letters. P(second letter is O) = 1/6 The combined probability is the product: 1/7 x 1/6 = 1/42 The other way to figure this out is to count the total possible outcomes. You have 7 tiles that could be picked for the first tile and 6 tiles that could be picked for the second tile. That's a total of 42 outcomes. Of these only 1 is the outcome of CO. P(CO) = 1/42 PART 2: On the first draw, there are 3 vowels out of 7 possible tiles P(first is a vowel) = 3/7 On the second draw, there are 2 vowels left out of 6 possible tiles. P(second is a vowel) = 2/6 = 1/3 Combined probability is the product: P(both are vowels) = 3/7 x 1/3 = 3/21 = 1/7
i) 1/7 * 1/6 = 1/42 ii) 3/7*2/6 = 1/7
Probability of CO: 1/(7*6) = 1/42 Combos of Vowels: 3*2 = 6 Probability of 2 Vowels: 6/42 = 3/21 = 1/7
