Question

'A' has three share in a lottery in which there are 3 prizes and 6 blanks 'B' has one share in a lottery in which there is 1 prize and 2 blanks. What is the ratio of probabilities of A's chance of winning a prize to that of B's chance of winning a prize.

• A. $12:7$
• B. $16:7$
• C. $7:16$
• D. $7:12$

Answer 1

The correct option is B $16:7$

Probability for A to loss = $\frac{{}^6{C}_3}{{}^9{C}_3}$

Probability for A to win = $1-\frac{{}^6{C}_3}{{}^9{C}_3}=1-\frac{6!}{3!3!}\times \frac{3!6!}{9!}=1-\frac{120}{504}=\frac{384}{504}=\frac{16}{21}$

Probability for B to loss = $\frac{{}^2{C}_1}{{}^3{C}_1}$

Probability for B to win = $1-\frac{{}^2{C}_1}{{}^3{C}_1}=1-\frac{2}{3}=\frac{1}{3}$

Hence the required ratio is

$\frac{16}{21}:\frac{1}{3}=16:7$