Question

1. A card drown at random from a well Shuffled pack of playting cards. Find the in trobability that the card drawn is
(i) A Non-face Card
(ii) A Card of Spades or an Ace
(iii) A Red King
(iv) Neither King nor a Queen
(v) Either a King or a Queen​

Answer 1

Step-by-step explanation:

There are 52 cards in total.

Hence, total Outcomes =52

(i) Probability of the card drawn is a card of spade or an Ace:

Total cards of Spade =13

Total Aces =4

Number of Aces of Spade =1

Therefore, 

Probability of the card drawn is a card of spade or an Ace:

5213+524−521=5216=134

(ii) Probability of the card drawn is a black king:

Total black kings: 2

Probability of the card drawn is a black king:

522=261

(iii) Probability of the card drawn is neither a jack nor a king

Total jacks =4

Total Kings =4

Probability of the card drawn is neither a jack nor a king:

1−524+4=1311

(iv) Probability of the card drawn is either a king or a queen:

Total Queens =4

Total Kings =4

Probability of the card drawn is either a king or a queen:

524+4=132

Answer 2

Total no. of cards = 52

(i)  No. of favorable outcome = 40

    P (non-face card) = $\frac{40}{52} = \frac{5}{6}$

(ii)  No. of favorable outcome = 20

     P (Spades/Ace) = $\frac{20}{52} = \frac{5}{12}$

(iii)  No. of favorable outcome = 2

      P (red king) = $\frac{2}{52} = \frac{1}{26}$

(iv)  No. of favorable outcome = 44

      P (neither king nor queen) = $\frac{44}{52} = \frac{11}{12}$

(v)   No. of favorable outcome = 8

      P (either king or queen) =  $\frac{8}{52} = \frac{1}{6}$