Question

The letters in the given list are written on tiles, one letter per tile. A, B, C, F, G, I, K, L, O, P, Q, T, V, W, X, Z The 16 tiles are placed in a bag and one is drawn randomly. Determine the probability of specific events using this situation.

Answer 1

(a)
`(1)/(16)`

(b)
`(1)/(8)`

(c)
`(3)/(16)`

(d)
`(15)/(16)`

Explanation:

The letters in each tile are:

A, B, C, F, G, I, K, L, O, P, Q, T, V, W, X, Z

Total Number of tiles n(S)=16

(a)The probability of drawing any one of the letters

The Probability of drawing any one of the letters
`=(1)/(n(S))=(1)/(16)`

(b)The probability of drawing either an "F" or "P" tile

P(Either an F or a P Tile) = P(drawing an F Tile )+P(drawing a P Tile)

`=(1)/(16)+(1)/(16)\\=(2)/(16)\\=(1)/(8)`

(c)The probability of drawing a vowel

The Vowel Tiles are: A,I,O

Number of Vowels =3

`\text{P(Drawing a vowel)}=(3)/(16)`

(d)The probability of not drawing a "Q" tile

`\text{P(Drawing a Q tile)}=(1)/(16)\\Therefore:\\\text{P(Not Drawing a Q tile)}=P(Q^c)=1-(1)/(16)\\=(15)/(16)`