What is the probability that the next cyclone to develop in Australian waters will cross the Qld coast
(Apply conditional and total probability).
Condition is cyclones that cross the Qld coast are only generated in the south pacific.
Cyclones generated in Australian waters is 10. Of these 10, 3 are generated in the south pacific. Cyclones that cross Qld coast is 2.
Thanks for everyones help.
To find the probability that the next cyclone to develop in Australian waters will cross the Qld coast, we can apply conditional and total probability.
Let's define the events:
A: Cyclones generated in Australian waters.
B: Cyclones that cross the Qld coast.
C: Cyclones generated in the south pacific.
We are given the following information:
P(C) = 3/10 (out of the 10 cyclones generated in Australian waters, 3 are generated in the south pacific)
P(B) = 2/10 (out of the 10 cyclones generated in Australian waters, 2 cross the Qld coast)
Using conditional probability, we can write:
P(B | C) = P(B ∩ C) / P(C)
P(B | C) represents the probability of cyclones crossing the Qld coast given that they are generated in the south pacific.
We know that P(B ∩ C) = P(B) * P(C)
Therefore:
P(B | C) = (2/10) / (3/10) = 2/3
Now, using total probability, we can calculate the probability of cyclones crossing the Qld coast:
P(B) = P(B | C) * P(C) + P(B | ~C) * P(~C)
Since cyclones generated in the south pacific are the only ones that cross the Qld coast, P(B | ~C) = 0. Therefore:
P(B) = (2/3) * (3/10) + 0 = 2/10 = 1/5
So, the probability that the next cyclone to develop in Australian waters will cross the Qld coast is 1/5 or 0.2, using the information provided.