# When a knight sets out on a quest he must choose a road to follow. probability question?

When a knight sets out on a quest he must choose a road to follow.

3 out of every 5 knights takes the High Road. The others take the Low Road.

Of the knights taking the High Road 80% are successful in their quest. The others fail.

Of the knights taking the Low Road 40% are successful in their quest. The others fail.

a) A knight is chosen at random. The probability that he will take the Low Road is ______

.

b) A knight is chosen at random. The probability that he will take the High road and succeed in his quest is ______

### 2 Answers

- 2 months ago
Let's say that you have 1000 knights. 600 will take the high road and 480 of those will be successful. 400 will take the low road and 160 of those will be successful

Part a is a little ambiguous. Is this before or after the knight has successfully completed his quest? If before, then there's a 0.4 probability that he will take the low road. If after, then there's a 160/(160 + 480) or 160/640, or 0.25 probability that he has taken the low road.

Part b is better: 480/1000 = 0.48

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- PuzzlingLv 72 months ago
Do you want probabilities as fractions or decimals or percentages?

Part (a):

3/5 of the knights take the High Road, so 2/5 take the Low Road.

P(knight takes the Low Road) = 2/5 (or 0.4 or 40%)

Part (b):

3/5 of the knights take the High Road

4/5 (or 80%) of those are successful.

3/5 * 4/5= 12/25

Or as decimals:

= 0.6 * 0.8

= 0.48

P(knight takes the High Road and is successful) = 12/25 (or 0.48 or 48%)

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