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)
1	0.201	6	0.027
2	0.264	7	0.008
3	0.078	8	0.082
4	0.037

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 0.818.
(type an integer or decimal rounded to three decimal places as needed.)
e. use the special addition rule and the probability distribution to determine the probability that the year had exactly eight major hurricanes.
the probability is 0.082.
(type an integer or decimal rounded to three decimal places as needed.)
f. use the special addition rule and the probability distribution to determine the probability that the year had between 2 and 4 major hurricanes, inclusive.
the probability is
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Identify relevant probabilities

We need to find $P(2\leq Y\leq4)$. From the table, $P(Y = 2)=0.264$, $P(Y = 3)=0.078$, $P(Y = 4)=0.037$.

Step2: Apply special - addition rule

The special - addition rule for mutually - exclusive events states that if $A$, $B$, and $C$ are mutually exclusive events, then $P(A\cup B\cup C)=P(A)+P(B)+P(C)$. Here, the events $Y = 2$, $Y = 3$, and $Y = 4$ are mutually exclusive. So $P(2\leq Y\leq4)=P(Y = 2)+P(Y = 3)+P(Y = 4)$.
$P(2\leq Y\leq4)=0.264 + 0.078+0.037$
$P(2\leq Y\leq4)=0.379$

Answer:

$0.379$