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A bag contains 3 white 5 black and 2 red balls all of the same shape and size.
A ball is drawn from the bag without looking into it, find the probability that the ball drawn is:
(i) a black ball.
(ii) a red ball.
(iii) a white ball.
(iv) not a red ball.
(v) not a black ball.

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In a bag 3 balls are white
2 balls are red
5 balls are black
Total number of balls = 3 + 2 + 5 = 10

(i) Number of possible outcome of one black ball = 10

And number of favourable outcome of one black ball = 5

∴ P(E) = Number of favourable outcome/Number of all possible outcome

= 5/10 = 1/2

(ii) Number of possible outcome of one red ball = 10

And number of favourable outcome = 2

∴ P(E) = Number of favourable outcome/Number of all possible outcome

= 2/10 = 1/5

(iii) Number of possible outcome of white ball = 10

And number of favourable outcome = 3

∴ P(E) = Number of favourable outcome/Number of all possible outcome

= 3/10

(iv) Number of possible outcome = 10

Number of favourable outcome

= 3 + 5 = 8

Not a red ball

∴ P(E) = Number of favourable outcome /Number of all possible outcome

= 8/10 = 4/5

(v) Number of possible outcomes = 10

Number of favourable outcome

not a black ball = 3 + 2 = 5

∴ P(E) = Number of favourable outcomes/Number of all possible outcomes

= 5/10 = 1/2

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