Question

Suppose we roll 2 dice. One die is red, and the other is green. Let event A = the sum is at most 5, and event B = the green die shows a 3.

a) Find P(A) b) Find P(B) c) Find P(A and B) d) Find P(AIB) e) Find P (BIA) f) Find P(A or B) g) Are events A and B independent?

Answer #1

You roll two six-sided fair dice. a. Let A be the event that the
first die is even and the second is a 2, 3, 4 or 5. P(A) = Round
your answer to four decimal places. b. Let B be the event that the
sum of the two dice is a 7. P(B) = Round your answer to four
decimal places. c. Are A and B mutually exclusive events? No, they
are not Mutually Exclusive Yes, they are Mutually...

Roll a pair of dice (one is red and the other is green). Let A
be the event that the red die is 4 or 5. Let B be the event that
the green die is 1. Let C be the event that the dice sum is 7 or
8.
Calculate P(A), P(B), P(C)
Calculate P(A|C), P(A|B)
Are the events A and C independent?
(20 points)
Suppose box 1 has four black marbles and two white marbles, and
box...

A pair of dice (one red and one green) is rolled. Think about
these events:
A= event that the sum of the numbers on the dice is 8
B= event that the red die shows the number 4
Find the following probabilities:
P(A)= ?
P(A ∩ B)=?
Suppose P(A) = 0.3, P(B )= 0.4, and P(A ∩ B) = 0.04
Find the following probabilities:
P(A ∩ Bc)=?
P(B ∩ Ac)=?
Please include work and answers!

Suppose you roll two six-sided dice at once, one yellow and the
other green.
Find the probability that: (1) The yellow die shows 3 and the
green shows
5. (2) The yellow die is even and the green shows 1. (3) The sum
of the
two numbers shown is 6.

Suppose two dice (one red, one green) are rolled. Consider the
following events. A: the red die shows 2; B: the numbers add to 5;
C: at least one of the numbers is 2; and D: the numbers do not add
to 12. Express the given event in symbols. HINT [See Example
5.]
The red die shows 2 and the numbers add to 5.
a) How many elements does it contain?

I
am going to roll two dice one time and look at the sum.
Let event A= sum is 8
Event B= sum is even
Event C= die 1 is a 3
1.Are events A and B Independent, dependent or mutually
exclusive? Why or why not?
2. Are events A and C independent, dependent or mutuallly
exclusive? Why or why not?
3. Are events B and C independent, dependent, or mutually
exclusive? Why or why not?

Suppose two dice (one red, one green) are rolled. Consider the
following events. A: the red die shows 1; B: the
numbers add to 3; C: at least one of the numbers is 1; and
D: the numbers do not add to 11. Express the given event
in symbolic form. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?

Two dice are thrown. Let E be the event that the sum of the dice
is even, let F be the event that the first die lands on 1, and let
G be the event that the sum is 8. Describe the events EF, E ∪ F, F
G, EF0 , EF G and find the probability that each occur.

You roll two six-sided fair dice.
a. Let A be the event that either a 3 or 4 is rolled first
followed by an odd number.
P(A) = Round your answer to four decimal places.
b. Let B be the event that the sum of the two dice is at most
7.
P(B) = Round your answer to four decimal places.
c. Are A and B mutually exclusive events?
No, they are not Mutually Exclusive
Yes, they are Mutually Exclusive
d....

You throw two fair dice, one green and one red, and observe the
numbers that came up.Take event A: the sum is 7, and event B: the
red die comes up even. Are these two events independent?

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