Question

Problem 2. Choose an integer at random from -3 to 6. The event A occurs if the chosen number is even, B occurs if the chosen number is smaller than 3; and C occurs if the chosen number is larger than 8. (a) List all the outcomes in Ω and in the events A, B and C. (b) Determine A', AUB, AG, A B, (c) Is A С B? Is B A? Are A and B mutually er clusive? (d) Compute: P(A), P(B). P(C), and P(Au B, P(AC) t n sent disasters, which are rare:

Answer 1

a) Possible outcomes

• Outcomes possible in $\Omega$ = {-3,-2,-1,0,1,2,3,4,5,6} i.e all the integers between -3 and 6 including both
• Outcomes possible in A = {-2,2,4,6}. Considering negative numbers as even and excluding 0 as 0 is neither even nor odd according to some
• Outcomes possible in B = {-3,-2,-1,0,1,2}
• Outcomes possible in C = NULL

b) $^{{A}'}$ = Outcomes in Not A = {-3,-1,0,1,3,5}

$A \cup B$ = Outcomes common to both A and B = {-2,2}

AC = NULL

A - B = A but not B = {4,6}

c) As all the elements of A are not present in B, hence A is not a subset of B.

  As all the elements of B are not present in A, hence B is not a subset of A.

No, A and B are not mutually exclusive as outcomes {-2,2} are common to both and hence A and B can occur at the same time.

d) P(A) = Favourable outcomes / Total outcome

= 4/10

= 0.4

P(B) = Favourable outcomes / Total outcome

= 6/10

= 0.6

P(C) = Favourable outcomes / Total outcome

= 0/10

= 0

P($A \cup B$) = Favourable outcomes / Total outcome

= 2/10

= 0.2

P(AC) = Favourable outcomes / Total outcome

= 0/10

= 0