Question

In: Statistics and Probability

Suppose you have a deck of 40 cards, containing 10 red cards and 30 black cards....

Suppose you have a deck of 40 cards, containing 10 red cards and 30 black cards. A player draws 7 cards from the deck and places them into their hand. The remaining deck of 33 cards has 5 red cards and 5 black cards in the top 10 cards. The other 23 cards in the remaining deck are unknown color. What is the probability of the player's hand having 0,1,2,3,4,5 red cards?

Solutions

Expert Solution

Total number of cards = 40

Total Number of red cards = 10

Total Number of black cards = 30

A player draws 7 cards from the deck and places them into their hand.

The remaining deck of 33 cards has 5 red cards and 5 black cards in the top 10 cards.

So,

Number of red cards remaining = 10 - 5 = 5

Number of black card remaining = 30 - 5 = 25

Total number of cards = 5 + 25 = 30

We have to draw 7 cards from 30 cards

Now

i)

the probability of the player's hand having 0 red cards

= probability of the player's hand having all the 7 cards black

ii)

The probability of the player's hand having 1 red cards

iii)

The probability of the player's hand having 2 red cards

iv)

The probability of the player's hand having 3 red cards

v)

The probability of the player's hand having 4 red cards

vi)

The probability of the player's hand having 5 red cards

orchestra answered 1 year ago
Next > < Previous

Related Solutions

Suppose that a deck of 52 cards contains 26 red cards and 26 black cards. Say...
Suppose that a deck of 52 cards contains 26 red cards and 26 black cards. Say we use the 52 cards to randomly distribute 13 cards each among two players (2 players receive 13 cards each). a. How many ways are there to pass out 13 cards to each of the two players? b. What is the probability that player 1 will receive 13 cards of one color and player 2 receive 13 cards of the other color?
Suppose that a deck of 52 cards contains 26 red cards and 26 black cards. Say...
Suppose that a deck of 52 cards contains 26 red cards and 26 black cards. Say we use the 52 cards to randomly distribute 13 cards each among two players (2 players receive 13 card each). a. How many ways are there to pass out 13 cards to each of the two players? b. What is the probability that player 1 will receive 13 cards of one color and player 2 receive 13 cards of the other color?
1. )A special deck of cards consists of  541 cards,  66 of which are red;  the rest are black....
1. )A special deck of cards consists of  541 cards,  66 of which are red;  the rest are black. If a card is selected at random and you look at it and remember what it is or write it down, then you  replace it into the same deck, shuffle the deck at least 7 times, then select a card. 7 shuffles is an adequate number to thoroughly mix the cards and prevent any doubts,   Find the probability that both cards are red.  leave answer as an...
choose exactly 7 red cards when you pick 10 cards from a deck.
choose exactly 7 red cards when you pick 10 cards from a deck.
A special deck of cards has 5 red cards, and 4 purple cards. The red cards...
A special deck of cards has 5 red cards, and 4 purple cards. The red cards are numbered 1, 2, 3, 4, and 5. The purple cards are numbered 1, 2, 3, and 4. The cards are well shuffled and you randomly draw one card. R = card drawn is red E = card drawn is even-numbered a. How many elements are there in the sample space? b. P(E) = Round to 4 decimal places.
A deck of 11 cards contains 4 red and 7 green cards. Shuffle this deck, then...
A deck of 11 cards contains 4 red and 7 green cards. Shuffle this deck, then deal 5 cards to Alice and 6 cards to Bob (without any replacement, of course). Let X be the number of red cards that Alice gets, and Y the number of red cards that Bob gets. (a) Write down the joint probability mass function of X and Y . (Write a formula rather than a table.) (b) Are X and Y independent? (c) Compute...
A “Remski Deck” is a deck of cards consisting of nine cards in each of 10...
A “Remski Deck” is a deck of cards consisting of nine cards in each of 10 denominations, A, 2, 3, 4, 5, 6, 7, 8, 9 and 10. In each denomination there are three cards in each of the three suits Harps: (H), Scythes (S) and Roses (R). So there are three different 2H, three different 10S, etc. for a total of 90 cards. A “hand” of eight cards is dealt. In a hand, the order the cards are dealt...
A “Remski Deck” is a deck of cards consisting of nine cards in each of 10...
A “Remski Deck” is a deck of cards consisting of nine cards in each of 10 denominations,A, 2, 3, 4, 5, 6, 7, 8, 9 and 10. In each denomination there are three cards in each of the three suits Harps: (H), Scythes (S) and Roses (R). So there are three different 2H, three different 10S, etc. for a total of 90 cards. A “hand” of eight cards is dealt. In a hand, the order the cards are dealt do...
A deck of playing cards contains 52 cards, half of which are red cards. What is...
A deck of playing cards contains 52 cards, half of which are red cards. What is the probability that the deal of a five-card hand provides: 1) No red cards? 2) At least 3 red cards? a) .325, .025 b) .325, .5 c) .5, .325 d) .025, .50 e) .5, .15
A handful of cards contains 4 black cards and 4 red cards. 3 cards are drawn...
A handful of cards contains 4 black cards and 4 red cards. 3 cards are drawn at random without replacement. The events A, B, C are defined as follows: • A ={more black cards than red cards are drawn} • B ={at least one black card is drawn} • C ={all the cards drawn are of the same color} (a) Compute P(A) (b) Compute P(B) (c) Compute P(C) (d) Compute P(A|B) (e) Are A and C independent?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT