form 7 probability.. [20點] 急急

1) A boy uses a home-made metal detector to look for valuable metallic objects on a beach. There is a fault in the machine which causes it to gives the signal of presence by only 95% of the metallic objects over which it passes and to fives the signal of presence by 6% of the non-metallic objects over which it passes. It is known that the objects over which the machine passes, 20% are metallic.

a) Find the probability that a given object over which the machine passes is metallic and the machine gives a signal (ANS: 0.19)

b) Find the probability of a signal being received by a boy for any given object over which te machine passes. (ANS: 0.248)

c) Find the probability that the boy has found a metal object when he receives a signal. (ANS: 0.798)
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2) Each of three boxes contains 10 balls which are completely identical apart from color.
Box A: 4 red and 6 white
Box B: 5 red and 5 white
Box C: 8 red and 2 white


One ball is drawn at random from box A, if it is red.
A ball is drawn at random from box B but if it is white
A ball is then drawn at random from box C.
The event that the ball from A is red is denoted by E.
The event that the second ball (drawn from box B or C) is red denoted by F

a) find P(F)
b) P(E∪F)
c) P(E | F)

Ans
a) 0.68
b) 0.88
c) 5/17