If a hurricane forms in the eastern half of the Bay of Bengal, there is a 76 percent chance that
it will strike the western coast of Maharashtra. From data gathered over the past 50 years, it
has been determined that the probability of a hurricane’s occurring in this area in any given
year is 0.85. What is the probability that a hurricane will occur in the eastern Bay of Bengal and strike Maharastra this year?
The current estimate is 76 percent.
To solve this problem, we can use the concept of conditional probability.
Let's define the events:
A = Hurricane occurs in the eastern Bay of Bengal
B = Hurricane strikes the western coast of Maharashtra
We are given:
P(A) = 0.85 (Probability of a hurricane occurring in the eastern Bay of Bengal in any given year)
P(B|A) = 0.76 (Probability of a hurricane striking the western coast of Maharashtra given that a hurricane occurs in the eastern Bay of Bengal)
We want to find:
P(A and B) = Probability of a hurricane occurring in the eastern Bay of Bengal and striking Maharashtra this year
By using the formula for conditional probability:
P(A and B) = P(B|A) * P(A)
Substituting the given values:
P(A and B) = 0.76 * 0.85
Calculating the product:
P(A and B) = 0.646
Therefore, the probability that a hurricane will occur in the eastern Bay of Bengal and strike Maharashtra this year is approximately 0.646 or 64.6%.
To calculate the probability that a hurricane will occur in the eastern Bay of Bengal and strike Maharashtra this year, we need to multiply the probability of a hurricane occurring in the eastern half of the Bay of Bengal by the probability of it striking the western coast of Maharashtra.
Given information:
- The probability of a hurricane occurring in the eastern half of the Bay of Bengal is 0.85.
- The probability of a hurricane striking the western coast of Maharashtra, given that it forms in the eastern half of the Bay of Bengal, is 0.76.
To find the probability, we multiply these two probabilities together:
Probability = 0.85 * 0.76
Probability = 0.646
Therefore, the probability that a hurricane will occur in the eastern Bay of Bengal and strike Maharashtra this year is 0.646, or approximately 64.6 percent.