Answer:
a) N(A∩B) = 0.9
b) N(A∩B) = 4.9
c) N(A or B) = 4.2
Step-by-step explanation:
Given that A and B each randomly, and independently, choose 3 of 10 objects;
P(A) = P(B) = 3/10 = 0.3
P(A') = P(B') = 1 - 0.3 = 0.7
a) chosen by both;
Probability of being chosen by both;
P(A∩B) = 0.3 × 0.3 = 0.09
Expected Number of objects being chosen by both;
N(A∩B) = P(A∩B) × N(total) = 0.09×10
N(A∩B) = 0.9
b) not chosen by either A or B;
Probability of not being chosen by either A or B;
P(A'∩B') = 0.7 × 0.7 = 0.49
Expected Number of objects being chosen by both;
N(A'∩B') = P(A'∩B') × N(total) = 0.49×10
N(A∩B) = 4.9
c) chosen by exactly one of A and B.
Probability of being chosen by exactly one of A and B
P(A∩B') + P(A'∩B) = 0.3×0.7 + 0.7 × 0.3 = 0.42
Expected Number of objects being chosen by both;
N(A or B) = 0.42 × 10
N(A or B) = 4.2
