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

Answer:

(a) $\frac{1}{16}$

(b)$\frac{1}{8}$

(c)$\frac{3}{16}$

(d)$\frac{15}{16}$

Step-by-step 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 $=\dfrac{1}{n(S)}=\dfrac{1}{16}$

(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)

$=\dfrac{1}{16}+\dfrac{1}{16}\\=\dfrac{2}{16}\\=\dfrac{1}{8}$

(c)The probability of drawing a vowel

The Vowel Tiles are: A,I,O

Number of Vowels =3

$\text{P(Drawing a vowel)}=\dfrac{3}{16}$

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

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