NCERT Class X Chapter 14: Probability Exercise 14.1 Question (14)
NCERT Class X Chapter 14: Probability Exercise 14.1 Question 14
Question:
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour
(ii) a face card
(iii) a red face card
(iv) the jack of hearts
(v) a spade
(vi) the queen of diamonds
Given:
A well-shuffled deck of 52 cards.
To Find:
The probability of getting: (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds
Formula:
Probability = Number of favorable outcomes Total number of outcomes
Solution:
(i) Probability of getting a king of red colour:
Number of kings of red colour = 2 (King of hearts and King of diamonds)
Total number of cards = 52
Probability = 2 52 = 1 26
(ii) Probability of getting a face card:
Number of face cards = 12 (4 Jacks + 4 Queens + 4 Kings)
Total number of cards = 52
Probability = 12 52 = 3 13
(iii) Probability of getting a red face card:
Number of red face cards = 6 (2 Jacks + 2 Queens + 2 Kings)
Total number of cards = 52
Probability = 6 52 = 3 26
(iv) Probability of getting the jack of hearts:
Number of jack of hearts = 1
Total number of cards = 52
Probability = 1 52
(v) Probability of getting a spade:
Number of spades = 13
Total number of cards = 52
Probability = 13 52 = 1 4
(vi) Probability of getting the queen of diamonds:
Number of queen of diamonds = 1
Total number of cards = 52
Probability = 1 52
Result:
(i) Probability of getting a king of red colour is \(\frac{1}{26}\),
(ii) Probability of getting a face card is \(\frac{3}{13}\),
(iii) Probability of getting a red face card is \(\frac{3}{26}\),
(iv) Probability of getting the jack of hearts is \(\frac{1}{52}\),
(v) Probability of getting a spade is \(\frac{1}{4}\),
(vi) Probability of getting the queen of diamonds is \(\frac{1}{52}\)
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