Chapter 10.2, Problem 22E

(a)

To determine

To calculate:

The probability value of the prediction future tropical type of cyclone in the northern

Hemisphere is a hurricane

Answer to Problem 22E

The probability value of the prediction future tropical type of cyclone in the northern hemisphere is a hurricane is $0.4616$

Explanation of Solution

Given information:

Type of tropical cyclone	Northern Hemisphere	Southern Hemisphere
Tropical depression	$100$	$107$
Tropical storm	$342$	$487$
Hurricane	$379$	$525$

Calculation:

In the given problem, there is random selection of the cyclone from the given groups and for the specific area.

Consider,

Hurricane: $H=379$

Tropical depression: $T_d=100$

Tropical storm: $T_s=342$

Here, total cyclones observed in the Northern Hemisphere are calculated as:

  $\begin{array}{l}n=H+T_d+T_s\\ n=379+100+342\\ n=821\end{array}$

In this draw need to predict future tropical type of cyclone in the Northern Hemisphere is a hurricane is calculated as:

  $\begin{array}{l}P\left(A\right)=\frac{H}{n}\\ P\left(A\right)=\frac{379}{821}\\ P\left(A\right)=0.4616\end{array}$

(b)

To determine

To calculate:

The probability value of the prediction future tropical type of cyclone in the Southern

Hemisphere is a hurricane

Answer to Problem 22E

The probability value of the prediction future tropical type of cyclone in the Southern hemisphere is a hurricane is $0.581$

Explanation of Solution

Given information:

Type of tropical cyclone	Northern Hemisphere	Southern Hemisphere
Tropical depression	$100$	$107$
Tropical storm	$342$	$487$
Hurricane	$379$	$525$

Calculation:

In the given problem, there is random selection of the cyclone from the given groups and for the specific area.

Consider,

Hurricane: $H_s=525$

Tropical depression: $T_{ds}=107$

Tropical storm depression: $T_{ss}=487$

Here, total cyclones observed in the Southern Hemisphere are calculated as:

  $\begin{array}{l}n=H_s+T_{ds}+T_{ss}\\ n=525+107+487\\ n=904\end{array}$

In this draw need to predict future tropical type of cyclone in the Southern Hemisphere is a hurricane is calculated as:

  $\begin{array}{l}P\left(B\right)=\frac{H_s}{n}\\ P\left(B\right)=\frac{525}{904}\\ P\left(B\right)=0.581\end{array}$