Question

If $P(A)=0.65$ , $P(B)=0.15$ then $P(A')+P(B')$ =
1. $1.5$
2. $1.2$
3. $0.8$
4. None of these

Answer 1

To solve this question you must know that if P(A) is the probability of the event A happening then P(A’) is the probability of the event not happening. Since an event either occurs or doesn’t occur there isn’t anything else that can happen therefore we can say that the sum of P(A) and P(A’) is always equal to one. Therefore you can find the value of P(A’) and P(B’) by subtracting P(A) and P(B) by one. And by adding both the values of P(A’) and P(B’) that we calculated we get the answer of the expression.
Complete step by step answer:
Now we know that the value of P(A) stands for the value of the event A occurring therefore
$P(A)=0.65$
Now we need to find the value of P(A’) which stands for the probability of event A not happening. To find this we can subtract P(A) from one therefore
$P(A')=1-0.65$
Subtracting we get the value of P(A‘) which is
$P(A')=0.35$
Similarly we need to find the value of P(B’) as we said that the value of P(B) stands for the value of the event B occurring therefore
$P(B)=0.15$
Now we can find the value of P(B’) by subtracting P(B) from one therefore
$P(B)=1-0.15$
Subtracting we get the value of P(B’) which is
$P(B')=0.85$
Now that we know the two values of P(A’) and P(B’) we can find the value of the needed expression by adding both values
$P(A')+P(B')=0.35+0.85$
Adding
$P(A')+P(B')=1.2$

So, the correct answer is “Option 2”.

Note: Probability is the possibility of a certain event occurring, it is the mathematical expression of the possibility. We must remember the fact that the probability of any event will always lie between zero and one. Hence, the probability of individual events will be less than one, but the sum can be greater than one but less than two.