Question

A box is filled with red cards, green cards, and blue cards. A card is chosen at random from the box. What is the probability that the card is not green? Write your answer as a fraction in simplest form.

Answer 1

The probability of not selecting a green card from a box with
`\(G\)` green cards among a total of
`\(T\)` cards is
`\((T - G)/(T)\)`. This represents the chance of choosing a non-green card from the box.

Define the Variables

Let
`\(G\)` represent the number of green cards in the box and
`\(T\)` be the total number of cards.

Calculate the Probability of Selecting a Green Card

The probability of choosing a green card is given by the ratio of the number of green cards to the total number of cards:

`\[ P(\text{green}) = \frac{\text{Number of green cards}}{\text{Total number of cards}} = (G)/(T) \]`

Find the Probability of Not Selecting a Green Card

The probability of not choosing a green card is the complement of the probability of selecting a green card. It can be found by subtracting the probability of getting a green card from 1:

`\[ P(\text{not green}) = 1 - P(\text{green}) \]`

`\[ P(\text{not green}) = 1 - (G)/(T) \]`

Express as a Simplified Fraction

To express this probability as a simplified fraction in terms of the total number of cards \(T\) and the count of green cards \(G\):

`\[ P(\text{not green}) = (T)/(T) - (G)/(T) = (T - G)/(T) \]`

This fraction
`(\( (T - G)/(T) \))` represents the probability of selecting a card that is not green, given the total number of cards in the box
`(\(T\))` and the count of green cards
`(\(G\))`.

complete the question

A box contains red, green, and blue cards. If a card is randomly chosen from the box, what is the probability that the selected card is not green? Express your answer as a simplified fraction in terms of the total number of cards, given the count of green cards among them.