Find the probability that the card drawn from the box.

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The box has cards numbered 14 to 99. Cards are mixed thoroughly and a card is drawn at random from the box. Find the probability that the card drawn from the box has
(i) an odd number
(ii) a perfect square number.

Solution:

Cards in a box are from 14 to 99 = 86
No. of total cards = 86
One card is drawn at random
Cards bearing odd numbers are 15, 17, 19, 21, …, 97, 99
Which are 43
(i) P(E) = \frac { Number\quad of\quad actual\quad events }{ Number\quad of\quad total\quad events }
= \\ \frac { 43 }{ 86 }
= \\ \frac { 1 }{ 2 }
(ii) Cards bearing number which are a perfect square
= 16, 25, 36, 49, 64, 81
Which are 6
P(E) = \frac { Number\quad of\quad actual\quad events }{ Number\quad of\quad total\quad events }
= \\ \frac { 6 }{ 86 }
= \\ \frac { 3 }{ 43 }

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is four times that of a red ball, find the number of balls in the bags.

Solution:

Number of red balls = 5
and let number of blue balls = x
Total balls in the bag = 5 + x
and that of red balls = \\ \frac { 5 }{ 5+x }
According to the condition,
\frac { x }{ 5+x } =4\times \frac { 5 }{ 5+x } =>\frac { x }{ 5+x } =\frac { 20 }{ 5+x }
x ≠ – 5
x = 20
Hence, number of blue balls = 20
and number of balls in the bag = 20 + 5 = 25

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