SOLUTION TO LAST MONTH'S QUIZ
1. 17/36
2. 5/17
3. 5/9
Notes
1. The probability that Smith walked, Smith said he walked, and
Jones also said he walked, which we denote by p(WWW),
= 1/4 * 2/3 * 2/3 = 4/36
Likewise, p(WBW) = 1/4 * 1/3 * 1/3 = 1/36
And p(BWW) = 3/4 * 1/3 * 2/3 = 6/36
And p(BBW) = 3/4 * 2/3 * 1/3 = 6/36
Total = 17/36
2. Probability Jones said Smith walked = 17/36 (as above).
Probability Smith walked and Jones said he walked
= p(WWW) + p(WBW) = 4/36 + 1/36 = 5/36
So required probability = 5/36 / 17/36 = 5/17
3. Similarly, p(WWW) + p(WBW) + p(BWB) + p(BBB)
= 4/36 + 1/36 + 3/36 + 12/36 = 20/36 = 5/9
