Question

The probability of raining on day 1 is 0.2 and on day 2 is 0.3. The probability of raining on both the days is
A) 0.2
B) 0.1
C) 0.06
D) 0.25

Answer 1

Hint : The probabilities of raining on both the days is given. The probability of rain on either day is independent of the other. The probability of raining on both the days is given by their intersection and when two events are independent, their intersection is the product of respective probabilities.

Complete step-by-step answer :
We have been given:
The probability of raining on day 1 is 0.2
$\Rightarrow P(1) = 0.2$
The probability of raining on day 2 is 0.3
$\Rightarrow P(2) = 0.3$
The probability of raining on the first day does not depend on that of the second day nor the probability of raining on the second day depends on that of the first day.
Thus, these events are independent as there is no dependency among the two events.
The probability of raining on both the days is calculated by the probability of their intersection i.e. the event of rain is applicable on both the days and it is given as:
$P\left( {1 \cap 2} \right)$
If the two events A and B are independent, then then their intersection is the product of probabilities of the two events. So:
$P\left( {1 \cap 2} \right) = P(1).P(2)$
Substituting the values, we get:
$P\left( {1 \cap 2} \right) = 0.2 \times 0.3 \\\ \Rightarrow P\left( {1 \cap 2} \right) = 0.06 \;$
Therefore, the probability of raining on both the days is $0.06$ and the correct option is C.
So, the correct answer is “Option C”.

Note : The events that are independent are also known as mutually exclusive events. While multiplying the decimal numbers, remember that the total numbers after the decimal on the left hand side and right hand side will be equal. When 0.2 is multiplied by 0.3, the total numbers after decimal are 2 (2 and 3 in both cases respectively). Thus in answer we required 2 numbers after decimal, so the answer becomes 0.06.