Eye radius of category 5 cyclones is 20Km. What is the probability that any randomly selected category 5 cyclone will cross the Qld coast such that the eye wall of the cyclone will pass over Cairns which is on a 3200Km section of Qld coast?
Cyclones generated in Australian waters is 10. Cyclones that crossed QLD coast 3.
Thanks for your help
30% cross the "Old" coast. 20/3200 or 1/160 is the probability the eye crosses a particular point on the coast. The overal probability is 0.3 *(1/160) = 1/533
To find the probability that a randomly selected category 5 cyclone will cross the Qld coast such that the eye wall will pass over Cairns, we need to use the information provided:
1. The eye radius of category 5 cyclones is 20 km.
2. The length of the Qld coast section is 3200 km.
3. Cyclones generated in Australian waters = 10.
4. Cyclones that crossed the Qld coast = 3.
First, let's calculate the ratio of the eye radius to the length of the Qld coast section.
Ratio = Eye radius / Qld coast length = 20 km / 3200 km = 0.00625.
This ratio represents the proportion of the Qld coast section that is covered by the eye radius of the cyclone.
Next, let's calculate the probability that a category 5 cyclone will cross the Qld coast.
Probability = (Number of cyclones that crossed the Qld coast) / (Total number of cyclones generated in Australian waters)
= 3 / 10
= 0.3.
This probability represents the likelihood of a cyclone generated in Australian waters crossing the Qld coast.
Finally, let's calculate the probability that the eye wall of the cyclone will pass over Cairns.
Probability = Probability of crossing the Qld coast * Ratio
= 0.3 * 0.00625
= 0.001875.
Therefore, the probability that any randomly selected category 5 cyclone will cross the Qld coast such that the eye wall will pass over Cairns is 0.001875 or 0.1875%.