Question

From a deck of playing cards, if the cards which show the factors of 10 and red coloured face cards are removed from the deck, then the probability of selecting a black coloured face card is

• A. $\frac{1}{17}$
  
• B. $\frac{3}{17}$
  
• C. $\frac{5}{17}$
  
• D. $\frac{19}{34}$
  

Answer 1

The correct option is B $\frac{3}{17}$


Factors of 10 : 2, 5, 10
Number of red coloured face cards (J, K, Q) = 3 × 2 = 6
Cards having the factors of 10 (2, 5, 10) and red coloured face card = (4 × 3) + (2 × 3)
= 12 + 6
= 18
$\therefore \text{Total number of remaining cards}=52–18$
= 34
Also, the total number of black coloured card of J, Q, K = 3 × 2 = 6
$\therefore \text{Required Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$=\frac{6}{34}$
$=\frac{3}{17}$
Hence, the correct answer is option (b).