SOLUTION: hello here is a exam question i have on my practice paper : Emilia picks up a chocolate at random from a box. All the chocolates in the box are identically wrapped. The proba

Question 457101: hello here is a exam question i have on my practice paper
:
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

Sophies box
P(Sophie picks a caramel)=P

(a)Work out the value of P.

(b)calculate the probability that Neither emilia nor sophie picks a caramel

Please help me with these and tell me step step instructions what to do and tips

thanks so much for your time

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
--------------------
Sophies box
P(Sophie picks a caramel)=P
--------------------
Note: The events are independent.
So, P(both pick caramel) = P(Emilia picks caramel)*P(Sophie picks caramel)
-----
(a)Work out the value of P.
Solve (5/8)P = (1/4)
p = (1/4)/(5/8)
P = 2/5
========================
(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
===================================================
Cheers,
Stan H.

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