Question

In: Statistics and Probability

5 cards are drawn at random from a standard deck. Give your answer as a fraction...

5 cards are drawn at random from a standard deck. Give your answer as a fraction or decimal out to at least 4 significant digits.

Find the probability that all the cards are hearts.

Find the probability that all the cards are face cards.
Note: Face cards are kings, queens, and jacks.

Find the probability that all the cards are even.
(Consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13)

Expert Solution

Probability of an event = Number of favorable outcomes / Total number of possible outcomes

Let n= 5 cards are drawn at a pack of 52 cards. i.e ⁵²C₅

n= ⁵²C₅

1) A= event of all the cards are hearts.

Total heart cards are 13.

m = ¹³C₅

P(A) = m / n

= ¹³C₅ / ⁵²C₅

ⁿC_r = n! / r ! (n-r) !

P(A) = 1287 / 2598960

= 0.0005

2) B= all the cards are face cards.

face cards- 4 kings, 4 queens, 4 jacks = 12

m = ¹²C₅

P(B) = m / n

= ¹²C₅ / ⁵²C₅

= 792 / 2598960

= 0.0003

3) C= all the cards are even.

(2,4,6,8,10,12).. hearts

(2,4,6,8,10,12)... Diamonds

(2, 4,6,8,10,12).... Clubs

(2,4,6,8,10,12)... Spades

Total cards =24

m = ²⁴C₅

P(C) = m / n

= ²⁴C₅ / ⁵²C₅

= 42504 / 2598960

= 0.0164

orchestra answered 2 years ago

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?

Two cards are drawn at random from a standard deck of 52 cards. The number of...

Two cards are drawn at random from a standard deck of 52 cards. The number of aces drawn is counted. Prepare a probability distribution for this random experiment. Hint: Find the probability that no aces are drawn, exactly one ace is drawn, etc.

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...

three cards are drawn at random without replacement from a standard deck of 52 playing cards....

three cards are drawn at random without replacement from a standard deck of 52 playing cards. Find the probability that the second and third cards are black? I seen the question online and answer is 850/1734 but i think it is wrong

Assume that 5 cards are dealt at random from a standard deck of 52 cards (there...

Assume that 5 cards are dealt at random from a standard deck of 52 cards (there are 4 suits in the deck and 13 different values (ranks) per each suit). We refer to these 5 cards as a hand in the rest of this problem. Calculate the probability of each of the following events when dealing a 5-card hand at random. (a) Exactly one pair: This occurs when the cards have numeric values a, a, b, c, d, where a,...

5. A hand of five cards is drawn without replacement from a standard deck. (a) Compute...

5. A hand of five cards is drawn without replacement from a standard deck. (a) Compute the probability that the hand contains both the king of hearts and the king of spades. (b) Let X = the number of kings in the hand. Compute the expected value E(X). Hint: consider certain random variables X1, . . . , X4. (c) Let Y = the number of “face” cards in the hand. Given is that E(Y ) = 15/13. Find the...

Two cards are drawn at random from an ordinary deck of 52 playing cards. If the...

Two cards are drawn at random from an ordinary deck of 52 playing cards. If the two cards display the same suit, you win $2. If they are the same color only, you win $1. Otherwise, you lose 50 cent. Calculate (a) the expected value of the amount you win; (b) the variance of the amount you win;

A card is drawn at random from a deck of cards so that the chance of...

A card is drawn at random from a deck of cards so that the chance of getting any card is equally likely. Given that the card was either an A; 2; 3; 4; 5 or 6, what is the chance that either the card was red or that the card was a number card (2-10)?

A card is drawn at random from a deck of cards. What is the probability that...

A card is drawn at random from a deck of cards. What is the probability that (a) it is a heart, given that it is red? (b) it is higher than a 10, given that it is a heart? (Interpret J, Q, K, A as 11, 12, 13, 14.) (c) it is a jack, given that it is red?

Two cards are drawn one after the other from a standard deck of 52 cards. (a)...

Two cards are drawn one after the other from a standard deck of 52 cards. (a) In how many ways can one draw first a spade and then a heart? (b) In how many ways can one draw first a spade and then a heart or a diamond? (c) In how many ways can one draw first a spade and then another spade? (d) Do the previous answers change if the first card is put back in the deck before...