Probability : PYQ
Q1. A coin is tossed once. Find the probability of getting a head. āĻāĻāĻž āĻŽā§āĻĻā§ā§°āĻž āĻāĻŦāĻžā§° āĻāĻ˛āĻŋāĻ¯āĻŧā§ā§ąāĻž āĻš'āĻ˛āĨ¤ Head (āĻŽā§ā§°) āĻĒā§ā§ąāĻžā§° āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤
Solution | āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
Total number of outcomes (āĻŽā§āĻ āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻĢāĻ˛āĻžāĻĢāĻ˛) = 2 (H, T)
Favourable outcomes (Head) (āĻ āĻ¨ā§āĻā§āĻ˛ āĻĢāĻ˛āĻžāĻĢāĻ˛ (Head)) = 1 (H)
Probability = Favourable Outcomes / Total Outcomes = 1 / 2
Probability of getting a Head (Head āĻĒā§ā§ąāĻžā§° āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž) = 1/2
Trick | āĻā§ā§°āĻŋāĻ
Probability = Favourable Outcomes ÷ Total Outcomes (āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž = āĻ āĻ¨ā§āĻā§āĻ˛ āĻĢāĻ˛āĻžāĻĢāĻ˛ ÷ āĻŽā§āĻ āĻĢāĻ˛āĻžāĻĢāĻ˛)
Coin (āĻŽā§āĻĻā§ā§°āĻž): H, T → 2 outcomes → Head = 1
Q3. A dice is rolled once. Find the probability of getting an even number. āĻāĻāĻž āĻĒāĻžāĻļāĻž āĻāĻŦāĻžā§° āĻ¨āĻŋāĻā§āĻˇā§āĻĒ āĻā§°āĻž āĻš'āĻ˛āĨ¤ āĻ¯ā§āĻā§āĻŽ āĻ¸āĻāĻā§āĻ¯āĻž āĻĒā§ā§ąāĻžā§° āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤
Solution | āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
Total number of outcomes (āĻŽā§āĻ āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻĢāĻ˛āĻžāĻĢāĻ˛)= 6 (1, 2, 3, 4, 5, 6)
Favourable outcomes (Even numbers)[āĻ āĻ¨ā§āĻā§āĻ˛ āĻĢāĻ˛āĻžāĻĢāĻ˛ (āĻ¯ā§āĻā§āĻŽ āĻ¸āĻāĻā§āĻ¯āĻž)] = 3 (2, 4, 6)
Ans | āĻāĻ¤ā§āĻ¤ā§°:
Probability of getting an even number (āĻ¯ā§āĻā§āĻŽ āĻ¸āĻāĻā§āĻ¯āĻž āĻĒā§ā§ąāĻžā§° āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž) = 1/2
Trick | āĻā§ā§°āĻŋāĻ
Probability = Favourable Outcomes ÷ Total Outcomes (āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž = āĻ āĻ¨ā§āĻā§āĻ˛ āĻĢāĻ˛āĻžāĻĢāĻ˛ ÷ āĻŽā§āĻ āĻĢāĻ˛āĻžāĻĢāĻ˛)
Even numbers on a dice = 2, 4, 6 (3 outcomes) [āĻĒāĻžāĻļāĻžāĻ¤ āĻ¯ā§āĻā§āĻŽ āĻ¸āĻāĻā§āĻ¯āĻž = 2, 4, 6 (3āĻāĻž āĻĢāĻ˛āĻžāĻĢāĻ˛)]
Shortcut | āĻāĻŽā§ āĻā§āĻļāĻ˛: 3 even numbers out of 6 faces (ā§ŦāĻāĻž āĻŽā§āĻā§° āĻāĻŋāĻ¤ā§°āĻ¤ ā§ŠāĻāĻž āĻ¯ā§āĻā§āĻŽ āĻ¸āĻāĻā§āĻ¯āĻž) ⇒ 3/6 = 1/2
Q4. A card is drawn from a deck of 52 cards. Find the probability of getting a heart. (ā§Ģā§¨ āĻāĻ¨ āĻ¤āĻžāĻā§° āĻāĻāĻ¨ āĻā§āĻā§° āĻĒā§°āĻž āĻāĻāĻ¨ āĻ¤āĻžāĻ āĻ¤ā§āĻ˛āĻž āĻš'āĻ˛āĨ¤ Heart (♥) āĻĒā§ā§ąāĻžā§° āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤)
Solution | āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
- Total number of outcomes (āĻŽā§āĻ āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻĢāĻ˛āĻžāĻĢāĻ˛) = 52
- Number of Hearts (Heart (♥) āĻ¤āĻžāĻā§° āĻ¸āĻāĻā§āĻ¯āĻž) = 13
Trick | āĻā§ā§°āĻŋāĻ
Shortcut | āĻāĻŽā§ āĻā§āĻļāĻ˛: One suit out of four suits (ā§ĒāĻāĻž āĻāĻŋāĻšā§āĻ¨ā§° āĻāĻŋāĻ¤ā§°āĻ¤ āĻāĻāĻž Heart ) = 1/4
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Q5. A card is drawn from a deck of 52 cards. Find the probability of getting a King. (ā§Ģā§¨ āĻāĻ¨ āĻ¤āĻžāĻā§° āĻāĻāĻ¨ āĻā§āĻā§° āĻĒā§°āĻž āĻāĻāĻ¨ āĻ¤āĻžāĻ āĻ¤ā§āĻ˛āĻž āĻš'āĻ˛āĨ¤ King (K) āĻĒā§ā§ąāĻžā§° āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤)
Solution | āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨Total number of outcomes (āĻŽā§āĻ āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻĢāĻ˛āĻžāĻĢāĻ˛)= 52
Total Kings in a deck (āĻāĻāĻ¨ āĻ¤āĻžāĻā§° āĻā§āĻāĻ¤ King (K))= 4
Probability = Favourable Outcomes / Total Outcomes â= 4â/52 = 1/13
Ans | āĻāĻ¤ā§āĻ¤ā§°: 1/13
Probability of getting a King (King (K) āĻĒā§ā§ąāĻžā§° āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻž) = 1/13
âTrick | āĻā§ā§°āĻŋāĻ
A deck has 52 cards and 4 Kings. (āĻāĻāĻ¨ āĻ¤āĻžāĻā§° āĻā§āĻāĻ¤ ā§Ģā§¨āĻāĻ¨ āĻ¤āĻžāĻ āĻĨāĻžāĻā§ āĻā§°ā§ ā§ĒāĻāĻ¨ King āĻĨāĻžāĻā§āĨ¤)
4/52 = 1/13
Shortcut | āĻāĻŽā§ āĻā§āĻļāĻ˛: Kings ÷ Total Cards (āĻŽā§āĻ āĻ¤āĻžāĻ) = 4 ÷ 52 = 1 ÷ 13
Important Formula | āĻā§ā§°ā§āĻ¤ā§āĻŦāĻĒā§ā§°ā§āĻŖ āĻ¸ā§āĻ¤ā§ā§° :
Probability always lies between 0 and 1. (āĻ¸āĻŽā§āĻāĻžā§ąāĻ¨āĻžā§° āĻŽāĻžāĻ¨ āĻ¸āĻĻāĻžāĻ¯āĻŧ 0 āĻā§°ā§ 1-ā§° āĻŽāĻžāĻāĻ¤ āĻĨāĻžāĻā§āĨ¤)