A bag contains 7 white, 5 black and 4 red balls. If two balls are draw

1.	A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that: (i) both the balls are white(ii) one ball is black and the other red (iii) both the balls are of the same colour
Answer» given: bag which contains 4 red, 5 black and 7 white balls Formula: P(E) = \(\frac{favorable\ outcomes}{total\ possible\ outcomes}\) two balls are drawn at random, therefore total possible outcomes are ¹⁶C₂ therefore n(S)=120 (i) let E be the event of getting both white balls E= {(W) (W)} n(E)= 7C₂= 21 P(E) = \(\frac{n(E)}{n(S)}\) P(E) = \(\frac{21}{120}\) = \(\frac{7}{40}\) (ii) let E be the event of getting one black and one red ball E= {(B) (R)} n(E)= ⁵C₁ ⁴C₁= 20 P(E) = \(\frac{n(E)}{n(S)}\) P(E) = \(\frac{20}{120}\) = \(\frac{1}{6}\) (iii) let E be the event of getting both balls of same colour E= {(B) (B)} or {(W) (W)} or {(R) (R)} n(E)= ⁷C₂+ ⁵C₂+⁴C₂= 37 P(E) = \(\frac{n(E)}{n(S)}\) P(E) = \(\frac{37}{120}\)

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that: (i) both the balls are white(ii) one ball is black and the other red (iii) both the balls are of the same colour

Answer»

given: bag which contains 4 red, 5 black and 7 white balls

Formula: P(E) = \(\frac{favorable\ outcomes}{total\ possible\ outcomes}\)

two balls are drawn at random, therefore

total possible outcomes are ¹⁶C₂

therefore n(S)=120

(i) let E be the event of getting both white balls

E= {(W) (W)}

n(E)= 7C₂= 21

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{21}{120}\) = \(\frac{7}{40}\)

(ii) let E be the event of getting one black and one red ball

E= {(B) (R)}

n(E)= ⁵C₁ ⁴C₁= 20

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{20}{120}\) = \(\frac{1}{6}\)

(iii) let E be the event of getting both balls of same colour

E= {(B) (B)} or {(W) (W)} or {(R) (R)}

n(E)= ⁷C₂+ ⁵C₂+⁴C₂= 37

P(E) = \(\frac{n(E)}{n(S)}\)

P(E) = \(\frac{37}{120}\)