Question 457101
 Emilia picks up a chocolate at random from a box.
All the chocolates in the box are identically wrapped.
The probability that she picks a caramel is 5/8. 
Sophie picks a chocolate at random from a different box.
All the chocolates in Sophie's box are identically wrapped.
The probability that she picks up a caramel is denoted by P. 
The probability that both Emilia and Sophie pick a caramel is 1/4 
Emilia's box 
P(emilia picks a caramal)=5/8 
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Sophies box
P(Sophie picks a caramel)=P 
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Note: The events are independent.
So, P(both pick caramel) = P(Emilia picks caramel)*P(Sophie picks caramel)
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(a)Work out the value of P.
Solve (5/8)P = (1/4)
p = (1/4)/(5/8)
P = 2/5
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(b)calculate the probability that Neither emilia nor sophie picks a caramel
P(Emelia does not pick caramel) = (3/8)
P(Sophie does not pick caramel) = (3/5)
P(neither picks are caramel) = (3/8)(3/5) = 9/40
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Cheers,
Stan H.