Question

Tags are attached to the left and right hind legs of a cow in a pasture. Let A1 be the event that the left tag is lost and the event that the right leg tag is lost. Suppose those two events are independent and A2 the event that the right leg tag is lost. Suppose those two events are independent and P(A1) = P(A2) = 0.3

a. Find the probability that at least one leg tag is lost.

b. Find the probability that exactly one tag is lost, given that at least one tag is lost.

c. Find the probability that exactly one tag is lost, given that at most one tag is lost.

Answer 1

Explanation:

Given that tags are attached to the left and right hind legs of a cow in a pasture. Let A1 be the event that the left tag is lost and the event that the right leg tag is lost. Suppose those two events are independent and A2 the event that the right leg tag is lost. Suppose those two events are independent and P(A1) = P(A2) = 0.3

a) the probability that at least one leg tag is lost

=
`P(A_1 U A_2)\\= P(A_1) + P(A_2)-{(A_1 \bigcap A_2)\\=P(A_1) + P(A_2)-{(A_1 )P(A_2)`

(since A1 and A2 are independent)

=0.3+0.3-0.09

=0.51

b) the probability that exactly one tag is lost, given that at least one tag is lost.

= P(one leg lost)/P(atleast one leg lost)

=
`P(atleast one leg lost)-P(Both lost)/0.51\\= (0.51-0.09)/(0.51) \\=14/17`

c) the probability that exactly one tag is lost, given that at most one tag is lost.