Answer: (a). 0.62 (b). 0.53
Step-by-step explanation:
Let us start by defining some events seen:
Given;
L rep the event that codes hidden Leia
BB represents the codes hidden in BB-8
H is the event that codes hidden by Hah
C-3PO rep the codes hidden in C3PO
Giving the probabilities, we have that
P(L) = probability that codes are hidden by Leia = 0.6
P(H) = probability that codes are hidden by Hah = 0.4
where P(BB/L) = 70/10 i.e 70%
P(C-3PO/L) = 1 - P(BB/L) = 1 - 7/10 = 3/10
Also, P(BB/H) = 1/2 = P(C-3PO/H)
We can say that Han Solo is likely to hide them in aceta BB-8 and C-3PO
To begin,
(a). The question tell us to find the probability that the codes are with BB-8.
First of all, we find P(BB).
P(BB) = P(L)*P(BB/L) + P(H)*P(BB/H)
solving this we get
P(BB) = 0.6*7/10 + 0.4*1/2 = 0.62
Therefore, the probability that the codes are with BB-8 = 0.62
(b). The second question says;
Given that the codes are with C-3PO, what is the probability the codes were hidden by Han Solo?
This tell us to find P(H/C-3PO)
P(H/C-3PO) = P(C-3PO/H)*P(H) / P(C-3PO/H) + P(C-3PO/L)*P(L)
inputting the values gives us;
P(H/C-3PO) = 1/2 * 0.4 / ( 1/2 *0.4 + 3/10 *0.6) = 0.53
SO we have that the probability the codes were hidden by Han Solo = 0.53
cheers I hope this was helpful!!
