Question

4. In the game Scrabble, there are a total of 100 tiles. Of the 100 tiles, 42 tiles have the vowels A, E, I, O, and U printed on them, 56 tiles have the consonants printed on them, and 2 tiles

are left blank.
a. If tiles are selected at random, what is the probability that the first tile drawn from the pile of 100 tiles is a vowel?
b. If tiles drawn are not replaced, what is the probability that the first two tiles selected are both vowels?
c. Event ???? is drawing a vowel, event ???? is drawing a consonant, and event ???? is drawing a blank tile. ????1 means a vowel is drawn on the first selection, ????2 means a consonant is
drawn on the second selection, and ????2 means a blank tile is drawn on the second selection. Tiles are selected at random and without replacement.
i. Find P(????1 and ????2).
ii. Find P(????1 and ????2).
iii. Find P(????1 and ????2).

Answer 1

Explanation:

Given that in the game Scrabble, there are a total of 100 tiles. Of the 100 tiles, 42 tiles have the vowels A, E, I, O, and U printed on them, 56 tiles have the consonants printed on them, and 2 tiles are left blank.

a. If tiles are selected at random, the probability that the first tile drawn from the pile of 100 tiles is a vowel =
`(42)/(100) =0.42`

b. If tiles drawn are not replaced, the probability that the first two tiles selected are both vowels =
`0.42^2 = 0.1764`

c. Event A is drawing a vowel, event B is drawing a consonant, and event C is drawing a blank tile. A1 means a vowel is drawn on the first selection, B2 means a consonant is drawn on the second selection, and C2 means a blank tile is drawn on the second selection. Tiles are selected at random and without replacement.

i. Find P(A1 and B2). =
`(42)/(100) *(56)/(99) \\=0.2376`

ii. Find P(A1 and c2). =
`(42)/(100) *(4)/(99) \\=0.0170`

iii. Find P(A1 and A2).=
`(42)/(100) *(41)/(99) \\=0.1739`