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Sol:
a. Consider a fair six-sided die as before, only in addition to the numbers 1 through 6 on each face,
we have the property that the even-numbered faces are colored red, and the odd-numbered
faces are colored green. Let event A be rolling a green face, and event B be rolling a 6. Then
, -



, -



It is can be seen that events A and B cannot simultaneously occur, since rolling a 6 means the
face is red, and rolling a green face means the number showing is odd. Therefore
, -
Hence the two events are mutually exclusive but not independent of each other.
b. Consider a fair coin and a fair six – sided die. Let event A be obtaining heads, and event B be
rolling a 6. Then we can reasonably assume that events A and B are independent, because the
outcome of one does not affect the outcome of the other. The probability that both A and B
occur is
, - , - , - (


) (


)



Since this value is not zero, then events A and B cannot be mutually exclusive.
c. Two mutually exclusive events cannot be independent.
d. A is the event in which, a two six – sided dies are rolled for a sum of 6 and B is the event in
which the event in A has a 2 on one of the dies.

Sol:
Plane 1 Plane 2 Plane 3 Plane 4
Small 5 10 5 0
Large 10 5 5 0
Venomous Non venomous Corals
Small 5 12 3
Large 10 10 0
1. Probability of living through this experience.
This happens in either of the following events
E1: The student travels in plane 4.
( )



E2: The student travels in Plane 1 (this itself has a probability of 0.25) unharmed.
This happens when all the large snakes in Plane 1 are nonvenomous and he is unharmed by the
small snakes
The probability for this is the product of the individual probabilities as they are mutually
exclusive events.
( )

The event of not being harmed by small snakes happens in either of the following events.
a. When all of them are nonvenomous
( )

b. When there is a mix up of corals and nonvenomous snakes.
( )


(

)
Hence the total probability is given by,
( )

(

)



( )





E3: The student travels in Plane 2 (this itself has a probability of 0.25) unharmed. This happens when all
the large snakes in Plane 2 are nonvenomous and he is unharmed by the small snakes. The probability
for this is the product of the...