Question

There are 14 white cabbages and x purple cabbages in a box.

A cabbage is selected at random.
The probability of taking a white cabbage from the box is 0.56.
Find the value of x.

Answer 1

x = 11

Explanation:

Given:

• 14 = number of white cabbages
• x = number of purple cabbages
• P(W) = 0.56

⇒ total number of cabbages = 14 + x

`\mathsf{Probability \ of \ an \ event \ occurring = (Number \ of \ ways \ it \ can \ occur)/(Total \ number \ of \ outcomes)}`

`\sf \implies P(W)=(number \ of \ white \ cabbages)/(total \ number \ of \ cabbages)`

`\sf \implies 0.56=(14)/(14+x)`

`\sf \implies 0.56(14+x)=14`

`\sf \implies 7.84+0.56x=14`

`\sf \implies 0.56x=6.16`

`\sf \implies x=11`