Answer to Question #321021 in Statistics and Probability for bob

Question

A box contains (𝑥+1) red marbles, (2𝑥+4) yellow marbles, and (4𝑥−6) green marbles

(i)

Find an expression, in terms of 𝑥, for the total number of marbles in the box.

(ii)

A marble is drawn at random from the box. Write down an expression, in terms of 𝑥, for the probability that the marble is red.

(iii)

Given that probability in part (ii) is 1/5, find the value of 𝑥.

Answer 1

(i)

The total number of marbles in the box:

$N=x+1+2x+4+4x-6=7x-1.$

(ii)

The probability that the drawn marble is red:

$P=\cfrac{x+1}{7x-1}.$

(iii)

$\cfrac{x+1}{7x-1}=\cfrac{1}{5},\\ 5x+5=7x-1,\\ 2x=6,\\ x=3.$