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Solve the following:
The ratio of Boys to Girls in a college is 3:2 and 3 girls out of 500 and 2 boys out of 50 of that college are good singers. A good singer is chosen what is the probability that the chosen singer is a girl?
Concept: undefined >> undefined
Solve the following:
Given three identical boxes, I, II, and III, each containing two coins. In box I, both coins are gold coins, in box II, both are silver coins and in box III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold?
Concept: undefined >> undefined
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Solve the following:
In a factory which manufactures bulbs, machines A, B and C manufacture respectively 25%, 35% and 40% of the bulbs. Of their outputs, 5, 4 and 2 percent are respectively defective bulbs. A bulbs is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B?
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that (2 − ω)(2 − ω2) = 7
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that (1 + ω − ω2)6 = 64
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that (1 + ω)3 − (1 + ω2)3 = 0
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that (2 + ω + ω2)3 − (1 − 3ω + ω2)3 = 65
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that (3 + 3ω + 5ω2)6 − (2 + 6ω + 2ω2)3 = 0
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that `("a" + "b"ω + "c"ω^2)/("c" + "a"ω + "b"ω^2)` = ω2
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that (a + b) + (aω + bω2) + (aω2 + bω) = 0
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that (a − b) (a − bω) (a − bω2) = a3 − b3
Concept: undefined >> undefined
If ω is a complex cube root of unity, show that (a + b)2 + (aω + bω2)2 + (aω2 + bω)2 = 6ab
Concept: undefined >> undefined
If ω is a complex cube root of unity, find the value of `ω + 1/ω`
Concept: undefined >> undefined
If ω is a complex cube root of unity, find the value of ω2 + ω3 + ω4
Concept: undefined >> undefined
If ω is a complex cube root of unity, find the value of (1 + ω2)3
Concept: undefined >> undefined
If ω is a complex cube root of unity, find the value of (1 − ω − ω2)3 + (1 − ω + ω2)3
Concept: undefined >> undefined
