Andy is not a very good navigator. When he enters a small town, the probability that he gets lost and cannot find the correct road to continue his journey, is 0.2. When he enters a large town, the probability that he does not find the correct exit road is 0.25. He starts on a journey that passes through two small towns followed by one large town. Draw a tree diagram to represent this info and use it to find the probability that
a)he reaches th second small town and leaves it on the correct road
b)he reaches the large town but fails to find the correct exit road.
plz help (any explanations wud be great)
town 1
right .8 wrong .2 (lost)
town 2
right .8 wrong .2 (lost)
city
right .75 wrong .25 (lost)
for part a
branches = right .8 * right .8 so .64
for part b
branches = right .8 * right .8 * wrong .25 so .64/4 = .16
To draw a tree diagram, we will start by representing Andy's journey. His journey passes through two small towns and one large town.
Step 1: Draw a line representing the starting point of the journey.
O
Step 2: Branch off from the starting point to represent the first small town.
O
|
S1
Step 3: From the first small town, branch off to represent the second small town and the correct road to leave it.
O
|
S1
|
S2 (C)
Step 4: From the second small town, branch off to represent the incorrect road.
O
|
S1
|
S2 (C)
|
S2 (I)
Step 5: From the first small town, branch off to represent the large town and the correct exit road.
O
|
S1
|
S2 (C)
|
S2 (I)
|
L (C)
Step 6: From the large town, branch off to represent the incorrect exit road.
O
|
S1
|
S2 (C)
|
S2 (I)
|
L (C)
|
L (I)
Now that we have the tree diagram, we can find the probability for each event.
a) The probability that Andy reaches the second small town and leaves it on the correct road can be found by multiplying the probabilities of each event along the path: S1 -> S2 (C).
P(S1 -> S2 (C)) = P(S1) x P(S2 (C)) = 0.2 x 0.2 = 0.04
Therefore, the probability that Andy reaches the second small town and leaves it on the correct road is 0.04.
b) The probability that Andy reaches the large town but fails to find the correct exit road can be found by multiplying the probabilities of each event along the path: S1 -> L (I).
P(S1 -> L (I)) = P(S1) x P(L (I)) = 0.2 x 0.25 = 0.05
Therefore, the probability that Andy reaches the large town but fails to find the correct exit road is 0.05.