Question

In​ gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For​ example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is​ 3, the odds of winning are​ 2:3 (read​ "2 to​ 3") or two thirds . ​(Note: If the odds of winning are two thirds ​, the probability of success is two fifths ​.) A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is not a spade.

Answer 1

Answer:

The odds that it is not a spade is 39:13 or 3:1.

Step-by-step explanation:

Total number of cards in a standard deck = 52

Total number of cards of each suit(club, spade, heart, diamond) = 13

Number of spade card = 13

Number of non-spade cards = 52 - 13 =39

The odds that a card is picked at random from a standard deck of 52 is not a spade is

$odds=\frac{\text{Total outcomes of non-spade cards}}{\text{Total outcomes of spade cards}}$

$odds=\frac{39}{13}$

On simplification we get

$odds=\frac{3}{1}$

Therefore, the odds that it is not a spade is 39:13 or 3:1.

Answer 2

Using the principle of odds representation in probability, the odds that a card chosen is not spade ls 3 : 1

• The total Number of cards = 52

• Number of spades = 13

Not spade = (total number of cards - number of spades)

Not spade = (52 - 13) = 39

The odds of not picking a spade can be represented thus :

• Not spade : Spade

• 39 : 13 = 3 : 1

Therefore, the odds of not choosing a spade is 3 : 1

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