Question

Rabies is a viral disease of mammals transmitted through the bite of a rabid animal. The virus infects the central nervous system, causing encephalopathy and ultimately death. The Florida Department of Health reports the distribution of documented cases of rabies for all of 2004:

Species Racoon Fox Bat Other
Probability 0.55 0.11 0.04 X
(a) What probability should replace X in the distribution? Please use 2 decimal places.
(b) What is the probability that a reported case of rabies is not a raccoon? Please use 2 decimal places.
(c) What is the probability that a reported case of rabies is either a bat or a fox? Please use 2 decimal places.

Answer 1

(a) The value of x is 0.30.

(b) The probability that a reported case of rabies is not a raccoon is 0.45.

(c) The probability that a reported case of rabies is either a bat or a fox is 0.15.

Explanation:

Denote the events as follows:

R = reported case of rabies is a raccoon

F = reported case of rabies is a fox

B = reported case of rabies is a bat

O = reported case of rabies is a some other animal.

The data provided is:

P (R) = 0.55

P (F) = 0.11

P (B) = 0.04

P (O) = x.

(a)

A property of a probability distribution is that the sum of all individual properties is 1.

That is,
`\sum P(X)=1`

Compute the value of x as follows:

`\sum P(X)=1\\P(R)+P(F)+P(B)+P(O)=1\\0.55+0.11+0.04+x=1\\0.70+x=1\\x=1-0.70\\x=0.30`

Thus, the value of x is 0.30.

(b)

The probability of the complement of an event is the probability of its not happening.

`P(A^(c))=1-P(A)`

Compute the probability that a reported case of rabies is not a raccoon as follows:

`P(R^(c))=1-P(R)\\=1-0.55\\=0.45`

Thus, the probability that a reported case of rabies is not a raccoon is 0.45.

(c)

Compute the probability that a reported case of rabies is either a bat or a fox as follows:

`P(B\cup F)=P(B)+P(F)\\=0.11+0.04\\=0.15`

Thus, the probability that a reported case of rabies is either a bat or a fox is 0.15.