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.

(a)

(b)

(c)

(d)

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

(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)

(c)The probability of drawing a vowel

The Vowel Tiles are: A,I,O

Number of Vowels =3

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

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form