The probability of drawing two red balls from a bag containing 8 white and 5 red balls is

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A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that:i All the three balls are white.ii All the three balls are red.iii One ball is red and two balls are white.

Solution

Total number of balls = 8 + 5 = 13
Total number of events for drawing 3 balls = 13C3
(i) Total number of events for getting white balls = 5C3
P(all 3 balls white) = favourable outcomestotal outcomes=5C313C3
=5!3!×2!×3!×10!13!
⇒P(all 3 balls white)=5143

(ii) Favourable number of events for getting red balls = 8C3

P(all 3 balls red) = favourable outcomestotal outcomes=8C313C3
=8!3!×5!×3!×10!13!
⇒P(all 3 balls red)=28143

(iii) Favourable number of events for getting 1 red ball = 8C1

Favourable number of events for getting 2 white balls = 5C2
P(1 red and 2 white balls) = favourable outcomestotal outcomes=8C1×5C213C3
=8!1!×7!×5!2!×3!×3!×10!13!
⇒P(all 3 balls red)=40143

Mathematics

RD Sharma XI (2019)

All

Gate Exam Numerical Ability Probability

• (8c2+6c2)/14c2=43/91
• 10 years agoHelpfull: Yes(17) No(0)
• probability of drawing two balls of white colour is (8/14)*(7/13) = 56/182 probability of drawing two balls of red colour is (6/14)*(5/13) = 30/182

  The probability of drawing two balls of same colour is 56/182 + 30/182 = 86/182 = 43/91

• 10 years agoHelpfull: Yes(16) No(5)
• ans=43/91 E(n)=8c2+6c2 s(n)=14c2

  P(n)=E(n)/S(n)=43/91

• 10 years agoHelpfull: Yes(5) No(0)
• (8C2+6C2)/14C2=43/91
• 9 years agoHelpfull: Yes(0) No(0)
• c. 28/91+15/91
• 7 years agoHelpfull: Yes(0) No(0)
• 43/91, Its 8c2+6c2/14c2
• 6 years agoHelpfull: Yes(0) No(0)
• n(S)={14C2}= 91 n(E)={8C2+6C2}= 43

  P(E)= 43/91

• 4 years agoHelpfull: Yes(0) No(0)