A set of 5 cards, each labeled with the letters A, B, C, D and E, is placed in a hat and two selected at random without replacement. Find the probability of getting D and E.
Answer: 1/10
Thanks for any help
You are choosing pairs from 5 cards
= C(5,2) = 10
the pair of DE is one of those, so
prob(DE) = 1/10
Why did the cards go to therapy? Because they couldn't get over their "D" and "E" issues! Well, if we want to find the probability of selecting D and E, we need to find the number of favorable outcomes divided by the number of possible outcomes. In this case, there are 5 cards in total, and we want to select D and E. Since we're selecting without replacement, there will only be 4 cards left after the first selection. So, the number of favorable outcomes is 1 (getting D) times 1 (getting E) which equals 1. The number of possible outcomes is 5 (total number of cards) times 4 (remaining cards), which equals 20. Therefore, the probability of getting D and E is 1/20. Keep calm and carry on calculating!
To find the probability of getting D and E, we first need to determine the total number of possible outcomes when selecting two cards out of the five.
Step 1: Calculate the total number of possible outcomes:
When selecting two cards out of five without replacement, we can use the combination formula, which is denoted by "nCr."
The combination formula nCr is given by:
nCr = n! / (r! (n-r)!)
In this case, n represents the total number of cards (5) and r represents the number of cards being selected (2).
Therefore, the number of possible outcomes is calculated as follows:
5C2 = 5! / (2! (5-2)!)
= 5! / (2! 3!)
= (5 x 4 x 3!) / (2! x 3!)
= (5 x 4) / (2 x 1)
= 10
So, the total number of possible outcomes is 10.
Step 2: Calculate the number of favorable outcomes:
Since we want to select cards labeled D and E, there is only one favorable outcome.
Step 3: Calculate the probability:
The probability of an event is given by the formula:
Probability = Favorable outcomes / Total outcomes
In this case, the probability of selecting cards D and E is calculated as follows:
Probability = 1 (favorable outcomes) / 10 (total outcomes)
= 1/10
Therefore, the probability of getting D and E is 1/10.
I hope this helps! Let me know if you have any further questions.
To find the probability of getting D and E, we need to determine the number of favorable outcomes (where D and E are selected) and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes
Since there are 5 cards in total and we want to select D and E, there is only 1 card labeled D and 1 card labeled E. Therefore, the number of favorable outcomes is 1.
Step 2: Determine the total number of possible outcomes
To find the total number of possible outcomes, we need to calculate the number of ways to select 2 cards out of 5. This can be done using the combination formula, which is expressed as:
nCr = n! / (r! * (n-r)!)
In this case, n = 5 (the total number of cards) and r = 2 (the number of cards we want to select).
Thus, the total number of possible outcomes is:
5C2 = 5! / (2! * (5-2)!) = (5 * 4 * 3 * 2 * 1) / ((2 * 1) * (3 * 2 * 1)) = 10
Step 3: Calculate the probability
Finally, to calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 10
= 1/10
Therefore, the probability of selecting D and E is 1/10.