Question

1 of the answers is not correct. when knights set out on quests they 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 the knight will take the low road is .40. b) a knight is chosen at random. the probability that the knight will take the high road and succeed in the quest is .48. c) a knight is chosen at random. the probability that the knight will succeed in the quest is . hint draw a probability tree. the first set of branches should tell which road the knight chooses.

Explanation:

Step1: Identify probabilities of road - choice

The probability of taking the High Road $P(H)=\frac{3}{5}=0.6$, and the probability of taking the Low Road $P(L)=0.4$.

Step2: Identify conditional probabilities of success

The probability of success given taking the High Road $P(S|H)=0.8$, and the probability of success given taking the Low Road $P(S|L)=0.4$.

Step3: Use the law of total probability

The law of total probability formula is $P(S)=P(H)\times P(S|H)+P(L)\times P(S|L)$.
Substitute the values: $P(S)=(0.6\times0.8)+(0.4\times0.4)$.
First, calculate $0.6\times0.8 = 0.48$ and $0.4\times0.4=0.16$.
Then, $P(S)=0.48 + 0.16$.
$P(S)=0.64$.

Answer:

$0.64$