A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probabilities. (Enter the probabilities as fractions.)
P (two of hearts0 I got 1/52 correct
P ( two)I got 4/52 correct
P (heart)I am not sure.
you are correct on the first two. The last should also be no sweat.
There is only 1 2-hearts in the deck of 52
There are 4 twos in the deck.
So, how many hearts are there?
Also, just as advice, usually you will need to reduce your fractions for your final answers. 4/52 = 1/13
So, revisiting #2 and #3, there are 13 different numeric values, so getting a two has a 1/13 chance.
So, how many suits are there? Each is equally likely.
To find the probabilities, we need to know the number of favorable outcomes (the number of ways the event can occur) and the total number of possible outcomes.
1. P(two of hearts):
In an ordinary deck of cards, there is only one two of hearts. Therefore, the number of favorable outcomes is 1. Since there are a total of 52 cards in the deck, the total number of possible outcomes is 52. So, P(two of hearts) = 1/52.
2. P(two):
To find the probability of selecting a two, we need to determine how many twos are there in the deck. In a standard deck, there are four twos (hearts, diamonds, clubs, and spades). So, the number of favorable outcomes is 4. The total number of possible outcomes is still 52. Therefore, P(two) = 4/52, which can be simplified to 1/13.
3. P(heart):
To calculate the probability of selecting a heart, we need to determine how many hearts are there in the deck. In a standard deck, there are 13 hearts (including the two of hearts). So, the number of favorable outcomes is 13. The total number of possible outcomes remains 52. Hence, P(heart) = 13/52, which simplifies to 1/4.
Thus, the probabilities are:
P(two of hearts) = 1/52
P(two) = 1/13
P(heart) = 1/4.