# What is the theoretical probability of picking a fruit-flavored bean and not picking a cinnamon bean if there are 20 red, cinnamon-flavored beans; 25 yellow, lemon-flavored beans; 15 green,...

What is the theoretical probability of picking a fruit-flavored bean and not picking a cinnamon bean if there are 20 red, cinnamon-flavored beans; 25 yellow, lemon-flavored beans; 15 green, mint-flavored beans; 30 purple, grape-flavored beans; and 10 white, pineapple-flavored beans in a bag of 100 jelly beans.

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### 1 Answer

Let

F= Fruits =65

C= Cinnamon=20

`FnnbarC=` Fruits and not cinnamon

`FnnC=` FruitsĀ and cinnamon= 15 mint

`P(F)=P(FnnbarC)+P(FnnC)`

`65/100=P(FnnbarC)+15/100`

`P(FnnbarC)=65/100-15/100=50/100=1/2`