Question

The following information is taken from the 2019 Traffic Safety Report for Jefferson county. It looks at all collisions with animals and splits them up into two categories: collisions with domestic animals and collisions with wild animals.

Year	Domestic Animal	Wild Animal	Total
2015	4	28	32
2016	6	29	35
Total	10	58	67

Your friend says they got in a crash with an animal and they are about to tell you a story. Match each phrase to it's probability notation:
a. The probability of the animal being wild, given that it is 2015.  --- wild|2015 P(wild|2015) P(wild) 2015 P(2015|wild)
b. The probability that the collision was in 2015.  --- P(wild) P(2015) P(2015|collision) 2015 wild|2015

Find the following probabilities. Enter your answers with at least 2 decimal places

c. P(Domestic|2016) =
d. P(Wild)=

Answer 1

Explanation:-

Given data

year	Domestic animal	wild animal	total
2015	4	28	32
2016	6	29	35
total	10	57	67

a) The relative frequencies of above table

year	Domestic animal	wild animal	total
2015			0.48
2016			0.52
total	0.15	0.85	1

The sum of conditional probabilities is equal to one

P(2015) = P(domestic or 2015) +P(wild or 2015) = 0.06+0.42 =0.48

P(2016) = P(domestic or 2016) +P(wild or 2016) = 0.09+0.43 =0.52

c)

year	Domestic animal	wild animal	total
2015			0.48
2016			0.52
total	0.15	0.85	1

a)

b)

year	Domestic animal	wild animal	total
2015			0.48
2016			0.52
total	0.15	0.85	1

c)

The probability of domestic animal

= P( domestic and 2015) or P(domestic and 2016)

= 0.06 + 0.09 =0.15

The probability of wild animal

= P( wild and 2015) or P(wild and 2016)

= 0.42 + 0.43 =0.85