Question

In: Statistics and Probability

Prob 1 Using a standard deck of cards, calculate the following probabilties. (denote your answers in...

Prob 1 Using a standard deck of cards, calculate the following probabilties. (denote your answers in decimals) a) drawing

a) red queen

b) drawing two red queens

c) drawing a diamond or a king

d) drawing a red card or a black card

e) Are queens and kings mutually exclusive?

Solutions

Expert Solution

N = number of cards in a standard deck = 52.

Number of king cards = 4

Number of queen cards = 4

Number of red cards = 26

Number of black cards = 26.

Number of diamond cards = 13

Number of king cards = 4

Number of red queens = 2

a) P ( drawing a red queen ) = 2 / 52 = 1/26

b ) P ( drawing two red queen ) = ²C₂ / ⁵²C₂ = 1/1326=0.00075

c) A : drawing a diamond

P( A ) = 13/ 52 = 1/4

B: Drawing a king card

P ( B) = 4/52 = 1/13

P(Drawing a king of diamond) = = 1/52.

P ( drawing a diamong or king card ) = P ( A U B)

P( Drawing a diamond or a king) = 0.3076

d) C : drawing a Red Card

P ( Drawing a Red Card)= P ( C) = 26/52. =0 .5000

D : drawing a Black card

P (Drawing a black cards) = P(D) = 26/52 = 0.5000

Since C and D are mutually exclusive events.

P ( Drawing a red or a black card) = P ( C U D ) = P(C) + P(D)

= 0.5000 + 0.5000

= 1

P ( Drawing a red or a black card) = 1

e) E : drawing a king card

P ( E ) = 4 / 52 = 1/13

F : drawing a queen card

P(F) = 4/52 = 1/13.

Hence E and F are mutually exclusive.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

The following question involves a standard deck of 52 playing cards. In such a deck of...

The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...

Suppose three cards are drawn without replacement from a standard deck of cards. A standard deck...

Suppose three cards are drawn without replacement from a standard deck of cards. A standard deck of cards contains 52 cards, each card is one of 4 types (hearts, diamonds, spades, clubs) and cards within each type are labelled 2, 3, 4, …, 10, J, Q, K, A. Compute the probability for each of the following. a. All three cards selected is a Heart. b. All three cards selected is a King. c. None of the three cards is either...

PROBLEM 1. There are 12 cards in a standard deck of cards with faces on them,...

PROBLEM 1. There are 12 cards in a standard deck of cards with faces on them, namely the 4 Jacks, the 4 Queens, and the 4 Kings. Assume below that the deck is well shuffled. (a). If you deal 5 cards without replacement, what is the probability of getting no face cards? (b). If you deal 5 cards WITH replacement (each time replacing the previous card and shuffling before dealing the next card), what is the probability of getting no...

he following question involves a standard deck of 52 playing cards. In such a deck of...

he following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...

1. In the game of poker, five cards from a standard deck of 52 cards are...

1. In the game of poker, five cards from a standard deck of 52 cards are dealt to each player. Assume there are four players and the cards are dealt five at a time around the table until all four players have received five cards. a. What is the probability of the first player receiving a royal flush (the ace, king, queen, jack, and 10 of the same suit). b. What is the probability of the second player receiving a...

With a standard deck of 52 playing cards, are your chances of drawing an ace and...

With a standard deck of 52 playing cards, are your chances of drawing an ace and then a king better with or without "replacement"? Illustrate with computations.

Assume there is a new version of porker, still using a standard deck of 52 cards....

Assume there is a new version of porker, still using a standard deck of 52 cards. It requires hands of six cards. There are some types of hands to get in the Porker. How many diﬀerent hands are possible for each type? 1. There are 4 cards of one common value and 2 cards of another common value. 2. All six cards are from the same suit, with exactly one ace and with no king. 3. There are 3 cards of...

. If 2 cards are selected from a standard deck of cards. The first card is...

. If 2 cards are selected from a standard deck of cards. The first card is not replaced in the deck before the second card is drawn. Find the following probabilities: a) P(2 Aces) b) P(Queen of hearts and a King) c) P(Q of Hearts and Q of hearts )

You draw cards from a standard deck of 52 playing cards. There are 12 “face cards”...

You draw cards from a standard deck of 52 playing cards. There are 12 “face cards” in the deck (J, Q, or K). Let X be the number of drawings (with replacement) it takes until you get your ﬁrst face card. Let Y be the number of drawings (with replacement) it takes until you get your ﬁfth face card. Let Z be the number of face cards removed if you draw 10 cards without replacement. (a) Calculate P(X = 5)....

Four cards are drawn at random from a standard deck of 52 cards. a. What’s the...

Four cards are drawn at random from a standard deck of 52 cards. a. What’s the probability that at least one card is a 7? b. What’s the probability that 3 of the 4 cards are the same suit? c. What’s the probability that they are all the same suit?

Subjects