Respuesta :
Answer:
The correct answer is A. 0.42
Step-by-step explanation:
Probability that neither A nor B occurs
[tex]= P(\bar{A})\cdot P(\bar{B})\\= (1 - 0.3)\cdot (1 - 0.4)\\= 0.7 \cdot 0.6\\ = 0.42[/tex]
Hence, the required probability is 0.42 and the correct option is A
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given that
Probability of occurring of event A = 0.3
Probability of occurring of event B = 0.4
Since event A and B are independent events,
So,
[tex]P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.3\times 0.4\\\\P(A\cap B)=0.12[/tex]
As we know the probability rules :
[tex]PA\cup B)=P(A)+P(B)-P(A\cap B)\\\\PA\cup B)=0.4+0.3-0.12\\\\PA\cup B)=0.7-0.12\\\\PA\cup B)=0.58[/tex]
We need to find the probability that neither A or B occurs:
So,
[tex]P(A'\cup B')=1-P(A\cup B)\\\\P(A'\cup B')=1-0.58\\\\P(A'\cup B')=0.42[/tex]
Hence, Probability that neither A or B occurs is 0.42.
Therefore, Option 'A' is correct.
