Probability (using combination)
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The document provides examples of calculating probabilities of drawing balls from bags or cards from decks. In example 7, it calculates the probability of drawing two red balls, two white balls, or one red ball from a bag containing 4 red, 5 black and 3 white balls. In example 8, it calculates the probability of drawing all white balls or one of each color from a bag containing 4 red, 5 black and 6 white balls. In example 9, it calculates the probability of drawing 2 kings and 1 ace from a standard 52 card deck.
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Probability (using combination)
- 2. Example-7: A bag contains 4 red, 5 black and 3 white balls. Two balls are drawn from the bag. Find the probability that: (i) Both are red balls (ii) Both are white balls (iii) One is red ball Solution: n (S) = 12 C2 = 55 (i) Let A = Both are red balls n (A) = 4 C2 = 6 (ii) Let B = both are white balls n (B) = 3 C2 = 3 (iii) Let C = one is red ball n (C) = 4 C1 8 C1 = 4 8 = 32 ( ) ( ) ( ) 1091.0 55 6 Sn An AP === ( ) ( ) ( ) 0545.0 55 3 Sn Bn BP === ( ) ( ) ( ) 5818.0 55 32 Sn Cn CP ===
- 3. Example-8: A bag contains 4 red, 5 black and 6 white balls. Three balls are drawn from the bag. Find the probability that: (i) All the balls are white (ii) One of each colour Solution: n (S) = 15 C3 = 455 (i) Let A = all the balls are white n (A) = 6 C3 = 20 (ii) Let B = one of each colour n (B) = 4 C1 5 C1 6 C1 = 4 5 6 = 120 ( ) ( ) ( ) 0439.0 455 20 Sn An AP === ( ) ( ) ( ) 2637.0 455 120 Sn Bn BP ===
- 4. Example-9: Three cards are drawn at random from a deck of 52 playing cards. Find the probability of getting 2 kings and one ace from them. Solution: n (S) = 52 C3 = 22100 Let A = 2 kings and one ace card n (A) = 4 C2 4 C1 = 6 4 = 24 ( ) ( ) ( ) 0011.0 22100 24 Sn An AP ===