Question

a certain hurricane database extends back to 1851, recording among other data the number of major hurricanes (measuring at least a category 3) striking a certain region per year. the following table provides a probability - distribution for the number of major hurricanes, y, for a randomly selected year between 1851 and 2012. complete parts (a) through (f) below.

y	p(y = y)	y	p(y = y)
0	0.182	5	0.041
1	0.281	6	0.027
2	0.264	7	0.008
3	0.078	8	0.002
4	0.037

a. use random - variable notation to represent the event that the year had at least one major hurricane. select the correct choice below and fill in the answer box within your choice.
a. p( )
b. {y≥1}
b. use random - variable notation to represent the event that the year had exactly eight major hurricanes. select the correct choice below and fill in the answer box within your choice.
a. {y = 8}
b. p( )
c. use random - variable notation to represent the event that the year had between 2 and 4 major hurricanes, inclusive. select the correct choice below and fill in the answer box within your choice.
a. {2≤y≤4}
b. p( )
d. use the special addition rule and the probability distribution to determine the probability that the year had at least one major hurricane.
the probability is
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Recall the complement rule

The probability of an event $A$ is $P(A)=1 - P(A^c)$. The event of having at least one major - hurricane is the complement of having zero major - hurricanes.

Step2: Identify $P(Y = 0)$ from the table

From the given probability distribution table, $P(Y = 0)=0.182$.

Step3: Calculate $P(Y\geq1)$

Using the complement rule $P(Y\geq1)=1 - P(Y = 0)$. Substitute $P(Y = 0)=0.182$ into the formula: $P(Y\geq1)=1 - 0.182 = 0.818$.

Answer:

$0.818$