A single card is selected from an ordinary deck of cards. The sample space is shown in the following figure. Find the following probabilities. (Enter the answers either as fractions or as decimals rounded to three places.)

P(five of clubs) = Incorrect: Your answer is incorrect.
P(five) = Correct: Your answer is correct.
P(club) = Incorrect: Your answer is incorrect.
P(jack) = Correct: Your answer is correct.
P(spade) = answer is incorrect.
P(jack of spades) =
P(five and a jack) =
P(five or a jack) =
P(heart and a jack) =
P(heart or a jack)

5 of C = 1/52

5 = 4/52 =1/13
club = 1/4 = 13/52
jack = 4/52 =1/13
spade same as club
J of S, same as 5 of C
You only took one card. It can not be 5 and jack
five or jack 1/13 + 1/13 = 2/13
heart and jack is jack of hearts 1/52
Heart OR jack
draw Venn diagram
There are 13 hearts
There are 4 jacks, three of which are not hearts. The jack of hearts is the intersection of the sets, careful not to count it twice.
So out of the 52 cards
13 are Hearts and 3 more are jacks that are not hearts
total = 13+3 = 16
so
16/52 = 4/13

heart or jack = 1/4 + 3/52

A single card is selected from an ordinary deck of cards. The sample space is shown in the following figure. Find the following probabilities. (Enter the answers either as fractions or as decimals rounded to three places.) A single card is selected from an ordinary deck of cards. The sample space is shown in the following figure. Find the following probabilities. (Enter the answers either as fractions or as decimals rounded to three places.)

p(5 or club)

P(five of clubs) = 1/52

P(five) = 4/52 or 1/13
P(club) = 13/52 or 1/4
P(jack) = 4/52 or 1/13
P(spade) = 13/52 or 1/4
P(jack of spades) = 1/52
P(five and a jack) = 0/52 or 0
P(five or a jack) = 8/52 or 2/13
P(heart and a jack) = 0/52 or 0
P(heart or a jack) = 17/52 or 4/13

To find the probabilities, we need to first determine the total number of outcomes in the sample space, which is the number of cards in a standard deck, and then count the number of favorable outcomes for each event.

1. P(five of clubs):
The probability of drawing the five of clubs is 1 out of 52, as there is only one five of clubs in the deck.

2. P(five):
To find the probability of drawing a five, we need to count the number of fives in the deck. There are four fives (one in each suit: clubs, diamonds, hearts, and spades) in the deck. So the probability of drawing a five is 4 out of 52.

3. P(club):
To find the probability of drawing a club, we need to count the number of clubs in the deck. There are 13 clubs in total (one for each rank), so the probability of drawing a club is 13 out of 52.

4. P(jack):
To find the probability of drawing a jack, we need to count the number of jacks in the deck. There are four jacks (one in each suit) in the deck. So the probability of drawing a jack is 4 out of 52.

5. P(spade):
To find the probability of drawing a spade, we need to count the number of spades in the deck. There are 13 spades in total (one for each rank), so the probability of drawing a spade is 13 out of 52.

6. P(jack of spades):
There is only one jack of spades in the deck, so the probability of drawing the jack of spades is 1 out of 52.

7. P(five and a jack):
To find the probability of drawing both a five and a jack, we need to determine the number of cards that satisfy this condition. There is only one card that satisfies this condition, which is the jack of diamonds. So the probability of drawing both a five and a jack is 1 out of 52.

8. P(five or a jack):
To find the probability of drawing either a five or a jack, we need to count the total number of cards that satisfy this condition. There are five cards that satisfy this condition: the four fives (from different suits) and the jack of any suit. So the probability of drawing either a five or a jack is 5 out of 52.

9. P(heart and a jack):
To find the probability of drawing both a heart and a jack, we need to determine the number of cards that satisfy this condition. There is only one card that satisfies this condition, which is the jack of hearts. So the probability of drawing both a heart and a jack is 1 out of 52.

10. P(heart or a jack):
To find the probability of drawing either a heart or a jack, we need to count the total number of cards that satisfy this condition. There are 17 cards that satisfy this condition: the 13 hearts (from any rank) and the four jacks (from different suits). So the probability of drawing either a heart or a jack is 17 out of 52.

Note: The probabilities can be simplified or expressed as decimals if desired.