Answer :
To determine the probability that it does not rain on two consecutive days, let's follow these steps:
1. Identify the probability of rain on any given day:
The problem states that the probability of raining on any given day is 0.4.
2. Calculate the probability of no rain on any given day:
Since the probability of raining is 0.4, the probability of not raining (complement of raining) on a given day is:
[tex]\[ P(\text{not rain}) = 1 - P(\text{rain}) = 1 - 0.4 = 0.6 \][/tex]
3. Determine the probability of no rain on two consecutive days:
Since the days are independent events, the probability of not raining on two consecutive days can be found by multiplying the probability of not raining on each day:
[tex]\[ P(\text{not rain on two consecutive days}) = P(\text{not rain}) \times P(\text{not rain}) = 0.6 \times 0.6 = 0.36 \][/tex]
Therefore, the probability that it does not rain on two consecutive days is:
[tex]\[ 0.36 \][/tex]
The correct answer is B) 0.36.
1. Identify the probability of rain on any given day:
The problem states that the probability of raining on any given day is 0.4.
2. Calculate the probability of no rain on any given day:
Since the probability of raining is 0.4, the probability of not raining (complement of raining) on a given day is:
[tex]\[ P(\text{not rain}) = 1 - P(\text{rain}) = 1 - 0.4 = 0.6 \][/tex]
3. Determine the probability of no rain on two consecutive days:
Since the days are independent events, the probability of not raining on two consecutive days can be found by multiplying the probability of not raining on each day:
[tex]\[ P(\text{not rain on two consecutive days}) = P(\text{not rain}) \times P(\text{not rain}) = 0.6 \times 0.6 = 0.36 \][/tex]
Therefore, the probability that it does not rain on two consecutive days is:
[tex]\[ 0.36 \][/tex]
The correct answer is B) 0.36.
