Question

A fair six-sided die is tossed twice. Consider the following events:

1. A : First toss yields an even number.

2. B : Second toss yields an odd number.

3. C : Sum of two outcomes is even.

Find P(A), P(B), P(C), P(B ∩ C), P(C|B), P(C|A ∩ B) and P(B|C).

Answer #1

A coin is tossed twice. Consider the following events.
A: Heads on the first toss.
B: Heads on the second toss.
C: The two tosses come out the same.
(a) Show that A, B, C are pairwise independent but not
independent.
(b) Show that C is independent of A and B but not of A ∩ B.

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...

1. A fair die is tossed twice ,find the probability of
getting a 4 or 5 on the first toss and find the probability of
getting 1, 2 or 3 on the second toss?
2. Diana draws a card at random deck of cards without replacing the
card that she drawed , what is the probability that the first card
is a 3 and a second card is a diamond ?

We toss a fair coin twice, define A ={the first toss is head}, B
={the second toss is tail}, and C={the two tosses have different
outcomes}. Show that events A, B, and C are pairwise independent
but not mutually independent.

5. Suppose the six-sided die you are using for this
problem is not fair. It is biased so that rolling a 6
is three times more likely than any other roll. For this
problem, the experiment is rolling a six-sided die twice.
(A): What is the probability that one or both rolls are even
numbers (2, 4 or 6’s)?
(B): What is the probability that at least one of the rolls is
an even number or that the sum of...

Imagine rolling two fair 6 sided dice. the number rolled on the
first die is even and the sum of the rolls is ten. are these two
events independent?

Suppose you toss a fair coin three times. Which of the following
events are independent? Give mathematical justification for your
answer.
A=
{“heads on first toss”}; B=
{“an odd number of heads”}.
A=
{“no tails in the first two tosses”}; B=
{“no heads in the second and third
toss”}.

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 roll a six-sided die. Find the probability of each of the
following scenarios.
(a) Rolling a 6 or a number greater than 3
(b) Rolling a number less than 5 or an even number
(c) Rolling a 6 or an odd number
(a) P(6 or number greater than 3)=
(Round to three decimal places as needed.)

Die question:
We toss a fair 6-sided die until exactly 5 spots appear on the
top of the die.
a) Referring to Die, what is the probability that we first
obtain 5 spots atop the die on the third toss?
b) Referring to Die, what is the expected number of tosses until
the first 5 appears on top of the die?

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