यदि एक बॉक्स में 4 लाल गेंदें और 6 नीली गेंदें हैं, तो एक ही रंग की 2 गेंदों को चुनने की प्रायिकता क्या है?

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SSC CGL Tier-II ( JSO ) 2017 Official Paper ( Held On : 22 Feb 2018 )
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  1. 8/15
  2. 12/25
  3. 13/25
  4. 7/15

Answer (Detailed Solution Below)

Option 4 : 7/15
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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दिया गया है

लाल गेंद = 4 और नीली गेंद = 6

सूत्र

P(E) = P(E1) + P(E2)

nCr = n!/r!(n – r)!

गणना

2 लाल गेंदों के निकाले जाने की प्रायिकता

⇒ P(E1) = 4C2/10C2

2 नीली गेंदों के निकाले जाने की प्रायिकता

P(E2) = 6C2/10C2

⇒ P(E) = = 4C2/10C2 + 6C2/10C2

⇒ (4C2 + 6C2)/10C2

⇒ [4!/2!(4 – 2)! + 6!/2!(6 – 2)!]/10!/2!(10 – 2)!

⇒ (6 + 15)/10!/2! × 8!

⇒ (21 × 2)/(10 × 9)

⇒ 42/90

⇒ P(E) = 7/15

∴ समान क्रम की 2 गेंदों को चुनने की प्रायिकता 7/15 है।
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