Determine the probability that the pen taken out is a good one.

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12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

Solution:

Number of defective pens = 12
Number of good pens = 132
Total number of pens =12 + 132 = 144
Probability of good pen
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 132 }{ 144 }
= \\ \frac { 11 }{ 12 }

If the probability of winning a game is \\ \frac { 5 }{ 11 } , what is the probability of losing?

Solution:

Probability of winning game = \\ \frac { 5 }{ 11 }
⇒ P(E) = \\ \frac { 5 }{ 11 }
We know that P (E) + P (\overline { E } ) = 1
where P (E) is the probability of losing the game.
\\ \frac { 5 }{ 11 } + P (\overline { E } ) = 1
⇒ P (\overline { E } ) = 1- \frac { 5 }{ 11 }
= \\ \frac { 11-5 }{ 11 }
= \\ \frac { 6 }{ 11 }

Two players, Sania and Sonali play a tennis match. It is known that the probability of Sania winning the match is 0.69. What is the probability of Sonali winning?

Solution:

Probability of Sania’s winning the game = 0.69
Let P (E) be the probability of Sania’s winning the game
and P (\overline { E } ) be the probability of Sania’s losing
the game or probability of Sonali, winning the game
P (E) + P (\overline { E } ) = 1
⇒ 0.69 + P (\overline { E } ) = 1
⇒ P(\overline { E } ) = 1 – 0.69 = 0.31
Hence probability of Sonali’s winning the game = 0.31

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