Question

Paul has a set of 20 cards that each show a differentnumber, as shown below.Paul will randomly select one of these cards. What isthe probability that the card he selects will show anumber less than 9?

Answer 1

You have a deck of 20 cards numbered from 1 to 20.

If you draw a card at random, the set of possible outcomes is:

`\mleft\lbrace1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20\mright\rbrace`

Let "A" represent the event "draw a card at random and it has a number less than 9"

The possible outcomes from the deck that fulfill the condition stated for A are all cards with numbers less than 9:

`A=\mleft\lbrace1,2,3,4,5,6,7,8\mright\rbrace`

So out of the 20 cards, there are 8 cards with a number "less than 9"

The probability of drawing a card with a number less than 9 can be determined as the quotient between the favourable outcomes and the total number of outcomes:

Favorable outcomes: 8

Total outcomes: 20

`\begin{gathered} P(A)=(8)/(20)=(2)/(5) \\ P(A)=0.4 \end{gathered}`

The probability that a card is chosen at random has a number less than 9 is 0.4