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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.

Sagot :

semsee45

Answer:

x = 11

Step-by-step explanation:

Given:

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

⇒ total number of cabbages = 14 + x

[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]

[tex]\sf \implies P(W)=\dfrac{number \ of \ white \ cabbages}{total \ number \ of \ cabbages}[/tex]

[tex]\sf \implies 0.56=\dfrac{14}{14+x}[/tex]

[tex]\sf \implies 0.56(14+x)=14[/tex]

[tex]\sf \implies 7.84+0.56x=14[/tex]

[tex]\sf \implies 0.56x=6.16[/tex]

[tex]\sf \implies x=11[/tex]

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