A box contains 4 red and 5 blue similar rings. what is the probability of selecting at random two rings: i. having same colour ii. having different colours
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Given , 4 red rings and 5 blue rings
Sample space = 4 + 5 = 9 rings
1) prob. of same color of two rings :
case 1 : both rings red
prob. = ⁴C₂ . ⁵C₀ / ⁹C₂ = 6/36 = 1/6
case 2 : both rings blue
prob. = ⁵C₂ . ⁴C₀ / ⁹C₂ = 10 /36 = 5/18
So considering both cases prob = 1/6 + 5 /18 = 8/18 = 4 /9
2) both are different ; both taken simultaneously then ,
prob. = ⁴C₁ . ⁵C₁ / ⁹C₂ = 4 x 5 /36 = 5/9
Hope my solution is correct.
Sample space = 4 + 5 = 9 rings
1) prob. of same color of two rings :
case 1 : both rings red
prob. = ⁴C₂ . ⁵C₀ / ⁹C₂ = 6/36 = 1/6
case 2 : both rings blue
prob. = ⁵C₂ . ⁴C₀ / ⁹C₂ = 10 /36 = 5/18
So considering both cases prob = 1/6 + 5 /18 = 8/18 = 4 /9
2) both are different ; both taken simultaneously then ,
prob. = ⁴C₁ . ⁵C₁ / ⁹C₂ = 4 x 5 /36 = 5/9
Hope my solution is correct.
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