Question

Consider an experiment with a standard 52-deck from which one card is randomly selected and not replaced. Then a second card is randomly selected. Define the following events: Event A = The first card is a heart

Event B = The second card is a heart

a. Are these two events mutually exclusive? Why or Why not?

b. Are these two events independent? Why or why not?

Answer #1

**Solution:**

Consider an experiment with a standard 52-deck from which one
card is randomly selected and not replaced. Then a second card is
randomly selected. Define the following events:
Event A = The first card is a heart
Event B = The second card is a heart
a. Are these two events mutually exclusive? Why or Why not?
b. Are these two events independent? Why or why not?

Consider a standard 52-card deck from which one card is
randomly selected and not replaced. Then, a second card is randomly
selected. Define the two events as given. Complete parts a) and b)
below.
A = The first card is a club
B = The second card is a king
Are these two events mutually exclusive? Why or why not?
A.The events are not mutually exclusive. The event of selecting
a club card as the first card cannot occur at...

A card is randomly selected from a standard, 52-card deck. The
denomination on the card is recorded so that the resulting sample
space is {A, 2, 3, 4, 5, 6, 7, 8, 9, 10, K, Q, J}. (In other words,
we ignore the suits.) (a) (5 points) Given that the card selected
displays some number from 3 to 10 (inclusive), what is the
probability that the value on the card is not a multiple of 4? (b)
(5 points) Suppose...

An
experiment consists of randomly selecting a card from a stamdard
deck of 52. Event A is defined as the event tbat the card selected
is a spade.
- Give an example of an event B for this experiment that such
events A and B are mutually exclusive
-Give an example of an event C for the experiment such that
the events A and C are NOT mutually exclusive.

Two cards are chosen at random from a standard 52-card deck.
Consider the events: A = first card is the ace of spades B = second
card is the ace of spades. Suppose the two cards are selected with
replacement.
i. Are the events A and B independent? Why?
ii. Are the events A and B mutually exclusive? Why?
Now suppose the two cards are selected without replacement.
iii. Are the events A and B mutually exclusive? Why?
iv. Are...

A card is to be randomly selected from an ordinary deck of 52
cards. Consider the following events: A = ace, B = face card and C
= club
a. which pairs of events, if any, are mutually exclusive?
b. find (i) P(A or B) (ii) P(A or C) (iii) P(B or C)

1. If two cards are drawn at random in succession from a
standard 52-card deck without replacement and the second card is a
club card, what is the probability that the first card is king
card?
2. Let A and B be two events in a sample S. Under what
condition(s) is P(A l B) equal to P(B l A) ?
3. If two events A and B are mutually Exclusive. Can A and B be
Independent? Why or why...

For the experiment of drawing a single card from a standard
52-card deck, find (a) the probability of the following event,
and (b) the odds in favor of the following event.
Neither a heart nor a king or queen
(b) The odds, in simplified form, in favor of the event of the
card being neither a heart nor a king or queen are ----- to
-------

Consider randomly selecting a card from a standard 52 card
deck.
Define the following events A: select a 5
B: select a red card
C: select a card which has an odd number
Compute the following probabilities.
a) P(A)
b) P(C)
c) P(A or B)
d) P(A|C)
e) P(A|B)
f) P(B|A)
g) P(A and B)

A standard deck of cards contains 52 cards. One card is selected
from the deck. (a) Compute the probability of randomly selecting a
a heart heart or club club. (b) Compute the probability of
randomly selecting a a heart heart or club club or diamond diamond.
(c) Compute the probability of randomly selecting an an ace ace or
heart heart.

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