Question

A bag contains card numbered from 1 to 100. A card is drawn at random from the bag. Find the probability of that the
a) card bears a no. which is a multiple of 5.
b) card bears a no. which is greater than or equal to 80.​

Answer 1

${\pmb{\sf{\underline{\maltese \: \: Understanding \: the \: Question...}}}}$

This question says that there is a bag which contains card numbered from 1 to 100. From that bag, a card is drawn at random. We have to find out the probability of the following:

• Card bears a number which is a multiple of 5.

• Card bears a number which is greater than or equal to 80.

${\pmb{\sf{\underline{\maltese \: \: Given \; that...}}}}$

• There is a bag which contains card numbered from 1 to 100.

• From that bag, a card is drawn at random.

${\pmb{\sf{\underline{\maltese \: \: To \; find...}}}}$

• Card bears a number which is a multiple of 5.

• Card bears a number which is greater than or equal to 80.

${\pmb{\sf{\underline{\maltese \: \: Solution...}}}}$

• Card bears a number which is a multiple of 5 = 1/5

• Card bears a number which is greater than or equal to 80 = 1/5.

${\pmb{\sf{\underline{\maltese \: \: Using \; formula...}}}}$

Probability of an event =

$\star\;\boxed{\sf{\pink{\dfrac{ Favourable\; number\;of\; outcomes}{Total\; number\;of\; outcomes}}}}$

${\pmb{\sf{\underline{\maltese \: \: Full \; Solution...}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀Solution for part 1.

↝ Favourable number of outcomes are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100.

↝ Total favourable number of outcomes are 20.

↝ Total number of outcomes are 100.

$\star\;\boxed{\sf{\pink{\dfrac{ Favourable\; number\;of\; outcomes}{Total\; number\;of\; outcomes}}}}$

↝ 20/100 = 2/10 = 1/5

Henceforth, card bears a number which is a multiple of 5 = 1/5

⠀⠀⠀⠀⠀⠀⠀⠀⠀Solution for part 2.

↝ Favourable number of outcomes are 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 and 100.

↝ Total favourable number of outcomes are 20.

↝ Total number of outcomes are 100.

$\star\;\boxed{\sf{\pink{\dfrac{ Favourable\; number\;of\; outcomes}{Total\; number\;of\; outcomes}}}}$

↝ 20/100 = 2/10 = 1/5

Henceforth, card bears a number which is greater than or equal to 80 = 1/5.