2. In the Scrabble dictionary, there are a total number of 101 two-letter words

Question

2. In the Scrabble dictionary, there are a total number of 101 two-letter words (and I hate them with a passion!). Randomly select two letters (they can be identical) from the alphabet, what is the probability that it would form a Scrabble word? 3. Randomly sample 3 cards at once out of 10 numbered cards from 1 to 10 that are otherwise identical. (a) Determine the probability that the smallest number on the 3 cards sampled is 5. (b) Determine the probability that the largest number on the 3 cards sampled is 5. Out of 1500 light bulbs, exactly 400 of them are defective and 1100 are non-defective. Randomly select a batch of 200 light bulbs. (a) Determine the probability that exactly 90 in the batch sampled are defective. (b) Determine the probability that at least 2 of light bulbs in the sampled batch are defective. 5. (a) Show algebraically that C)-(-.) (b) Instead of using algebra, can you prove part (a) in two reasonably long sentences or less?

Explanation / Answer

2. Number of two letter combinations possible = 26 x 26 = 676

P(random 2 letters for a Scrabble word) = 101/676 = 0.1494

3. (a) P(smallest number is 5) = P(One card is 5 and other two cards are greater than 5)

= 1/10 x P(chosing 2 cards from 6 to 10 out of total 9 cards)

= 1/10 x 5C2/9C2

= 0.0278

(b) P(largest number on the cards sampled is 5 = P(one card is 5) x P(other two cards are smaller than 5)

= 1/10 x 4C2/9C2

= 0.0167

P.S: Please post different questions separately

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