Helen has a set of number cards numbered 1 thru 10. If Helena randomly draws two cards from the deck, what is the probability that she will draw an even number and then a five?
To find the probability of drawing an even number and then a five, we need to determine how many favorable outcomes there are and divide it by the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
There are 5 even numbers in the deck (2, 4, 6, 8, 10). Once an even number is drawn, there will be 9 cards left, and only 1 of them is a five. Therefore, there is 1 favorable outcome.
Step 2: Determine the total number of possible outcomes.
Since Helen is drawing two cards from a set of 10 numbers, there are 10C2 (combination) total possible outcomes.
The formula for combination is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen at a time.
Using the formula, we get 10C2 = 10! / (2! * (10-2)!) = 45 total possible outcomes.
Step 3: Calculate the probability.
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
Probability = favorable outcomes / total outcomes
Probability = 1 / 45
So, the probability that Helen will draw an even number and then a five is 1/45.
To find the probability of drawing an even number and then a five, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Helen has a set of number cards numbered from 1 to 10. Since she draws two cards from the deck, the total number of possible outcomes can be calculated using the combination formula nCr, where n is the total number of cards and r is the number of cards drawn.
In this case, n = 10 (total number of cards) and r = 2 (number of cards drawn).
Using the combination formula nCr = n! / (r! * (n - r)!), the total number of possible outcomes is:
10! / (2! * (10 - 2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45
Therefore, there are 45 possible outcomes.
Number of favorable outcomes:
To determine the number of favorable outcomes, we need to consider the following:
1. Helen needs to draw an even number first.
- There are 5 even numbers in the deck (2, 4, 6, 8, and 10).
2. After drawing an even number, Helen needs to draw a five.
- There is only one card with the number 5.
Therefore, there is 1 favorable outcome.
Probability:
The probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 45
To simplify the probability, we can convert it to a decimal or percentage:
Probability = 0.022 or 2.2%
Therefore, the probability that Helen will draw an even number and then a five is approximately 0.022 or 2.2%.