A system has 5 components, two of which are known to have a special marking stamped...
A system has 5 components, two of which are known to have a special marking stamped on the side. (The other 3 components are known not to have the marking). Components are checked one at a time until two of the unmarked components have been found.
a) draw a tree diagram for this experiment
b) what is the probability that both of the marked components are checked?
c) what is the probability that exactly one of the marked components is checked?
d) what is the probability that at least one marked component is checked?
Homework Answers
a) Tree diagram is given below
b) P(both marked components are checked) = (2/5 x 1/4 x 1) + (2/5 x 3/4 x 1/3 x 1) + (3/5 x 2/4 x 1/3 x 1)
= 0.1 + 0.1 + 0.1
= 0.3
c) P(exactly one of the marked components is checked) = (2/5 x 3/4 x 2/3) + (3/5 x 2/4 x 2/3)
= 0.2 + 0.2
= 0.4
d) P(at least one marked component is checked) = 1 - P(both are unmarked components)
= 1 - (3/5 x 2/4)
= 1 - 0.3
= 0.7
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