Question

You have 200 dice in a bag. One of the dice has a six on all sides so it will land on a six every time you roll it. The other 199 are normal dice with six sides, each with a different number. You randomly pick one of the dice from the bag and roll it three times. It lands on six all three times. What is the probability it is the die that always lands on six and what is the probability it is a normal die?

Answer 1

Answer:

Step-by-step explanation:

There are 200 dice out of which 199 are fair

Prob for 6 in one special die = 1 and

Prob for 6 in other die = 1/6

A1- drawing special die and A2 = drawing any other die

A1 and A2 are mutually exclusive and exhaustive

P(A1) = 1/200 and P(A2) = 199/200

B = getting 6

i) Required probability

= P(A1/B) = $\frac{P(A1B)}{P(A1B)+P(A2B)}$

P(A1B) = $\frac{1}{200} *1 = \frac{1}{200}$

P(A2B) = $\frac{199}{200}*\frac{1}{6}=\frac{199}{1200}$

P(B) = $\frac{205}{1200} =\frac{41}{240}$

P(A1/B) = $\frac{1/200}{41/240} =\frac{7}{205}$

P(A2/B) = $\frac{199/1200}{41/240} =\frac{199}{205}$