Question

If $A$ and $B$ are two independent events such that $P(A) = 0.40$, $P(B) = 0.50$. Find $P$ (neither $A$ nor $B$).
A. $0.90$
B. $0.10$
C. $0.2$
D. $0.3$

Answer 1

Take the given data and find the correlation between the given data and the required data by using the formula. As the given events are independent, find the complement of the events and then place its value and simplify for the required values.

Complete step by step answer:
Given that: $P(A) = 0.40$ and $P(B) = 0.50$.
P (neither A nor B) can be given by $= P(A' \cap B')$
Given that both the events $A$ and $B$ are Independent. Independent events are defined as those events whose occurrence does not depend on any other event. It does not have any connection to another event’s chances of happening or not happening.
$P(A' \cap B') = P(A').P(B')$
Place the given values in the above expression -
$P(A' \cap B') = (0.6).(0.5)$
Simplify the above expression finding the product of the above terms –
$\therefore P(A' \cap B') = 0.3$

Hence, the option D is the correct answer.

Note: Know the difference between the dependent and independent events and apply its concepts accordingly. When the given two events are independent then one event does not influence the probability of another event whereas, the dependent events influence the probability of the other events that is its occurrence is affected by the other events. Be careful while simplifying the decimal numbers when you multiply the two decimal numbers, count the total number of digits after the decimal point in both the numbers and shift the decimal number with the total digits in the resultant value.