Question

In a given experiment, there are four equally likely outcomes ξ1, ξ2, ξ3, ξ4 and two events A = {ξ1, ξ2} and B = {ξ2, ξ3}. Compute P [ABc], P [BAc], P [AB], P [A ∪ B].

Answer 1

four equally likely outcomes ξ1, ξ2, ξ3, ξ4 makes Universal set

U={ξ1, ξ2, ξ3, ξ4}

A = {ξ1, ξ2} and B = {ξ2, ξ3}

So., Ac = U-A = {ξ3, ξ4}

like wise Bc = U-B ={ξ1, ξ2, ξ3, ξ4}-{ξ2, ξ3} = {ξ1, ξ4}

So., P [ABc] = P[ABc] =P[{ξ1}] = 1/4 [i.e chances of ξ1 to come]

like wise P [BAc] = P[AcB] = P[{ξ3}] =1/4 &

P[AB]= P[AB] = P[{ξ2}] =1/4

now for P [A ∪ B] = P[ {ξ1, ξ2, ξ3}] = 3/4

Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!

answered by: anonymous