Bob and Dice

Probability Level 4

Bob, who is known to lie 3 out of 4 times, rolls a fair dice and says it is 6. What is the probability that the dice actually shows number 6 ??

The answer is 0.25.

2 solutions

Baby Googa
Apr 9, 2015

Case 1: Bob gets a $6$ and does not lie

The probability of getting a $6$ is $\frac{1}{6}$ , and the probability of Bob not lying is $\frac{1}{4}$ . So the total probability is $\frac{1}{6} * \frac{1}{4} = \frac{1}{24}$ .

Case 2: Bob doesn't get a $6$ and lies

The probability of not getting a $6$ is $\frac{5}{6}$ , and the probability of Bob lying is $\frac{3}{4}$ . We also have to multiply by $\frac{1}{5}$ because Bob won't always say $6$ when lying. So the total probability is $\frac{5}{6} * \frac{3}{4} * \frac{1}{5} = \frac{3}{24}$ .

By Bayes theorem, $\frac{\frac{1}{24}}{\frac{1}{24}+\frac{3}{24}} = \frac{1}{4} = \boxed{0.25}$

but it is menrtioned in the question that man reports six then why is it necessary to include those events when man doesn't report's a six.. i've figured out it using bayes theorem but got it wrong.

Priyesh Pandey - 6 years, 1 month ago

Harry Chan
May 9, 2015

It is given that he says it is 6. Then "The dice shows number 6" is equivalence to "He is not lying". So the answer is simply 1-0.75=0.25 Don't think too much :)

Bob and Dice

The answer is 0.25.

2 solutions

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