Question

What are the odds against choosing a blue marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?

Answer 1

Given,

The number of blue marbles in bag is 2.

The number of green marbles in bag is 1.

The number of white marbles in the bag is 7.

The number of red marbles in the bag is 4.

Required

The odd against in choosing the blue marbles from the bag.

The total number of marbles in the bag is,

`Total\text{ marbles = 2+1+7+4=14}`

The probability of choosing a blue marble is,

`P(blue)=(2)/(14)`

The probability of not chooisng the ble marble is.,

`\begin{gathered} P(not\text{ blue\rparen=}(14-2)/(14) \\ =(12)/(14) \end{gathered}`

The odd against in choosing the blue marbles from the bag.

`\begin{gathered} P(odds\text{ against blue\rparen=}\frac{P(not\text{ blue\rparen}}{P(blue)} \\ =(12)/(14)*(14)/(2) \\ =(12)/(2) \\ =12:2 \end{gathered}`

Hence , The odd against in choosing the blue marbles from the bag is 12 :2.