I MUST DRAW TWO CARDS WHOSE SUM IS NINE, FROM A STACK OF CARDS NUMBERED ONE THRU TEN. AFTER THE FIRST DRAW, I REPLACED THE CARD AND SHUFFLE THE STACK AGAIN FOR THE SECOND DRAW. WHAT IS THE CHANCE THAT MY TWO CARDS WILL HAVE A SUM OF NINE IF I DREW 10-TIMES.
MY ANSWER IS 20 DRAWS FOR THE NUMBER NINE TO BE CHOSEN. AM I CORRECT.
no, your answer does not answer the question.
how many ways can you get a sum of nine.
1,8
8,1
7,2
2,7
3,4
4,3
5,2
2,5
6,3
3,6
so 10 ways you can get a nine. The probability of each way is 1/10*1/10
so the probability to do this in ten times is 10*1/100= 1/10
First you have to decide which numbers equal 9
8,1
1,8
7,2
2,7
3,6
6,3
4,5
5,4
There are 8 possible combinations to equal 9. The deck has 10 cards to start. And after the 1st draw there are 10 cards again. All together there are 10 X 10 = 100 combinations total.
8/100 = 4/50 = 2/25. Odds are 2 out of every 25 tries.
To calculate the chance of drawing two cards with a sum of nine from a stack of cards numbered one through ten, we need to consider the total number of possible outcomes.
In this case, we'll use the concept of combinations to determine the number of favorable outcomes (pairs that sum up to nine).
There are multiple combinations of pairs that can sum up to nine:
- (1, 8)
- (2, 7)
- (3, 6)
- (4, 5)
- (5, 4)
- (6, 3)
- (7, 2)
- (8, 1)
So, there are a total of 8 favorable outcomes.
Since you draw two cards each time and the cards are replaced and shuffled before the next draw, we can treat each draw as an independent event.
The total number of possible outcomes for each draw is 10, as there are ten cards to choose from.
Now, let's calculate the probability of drawing two cards with a sum of nine on each draw:
Probability of drawing two cards with a sum of nine on each draw = (Number of favorable outcomes) / (Number of possible outcomes)
= 8 / 10
= 4/5
Therefore, the chance of drawing two cards with a sum of nine in each of the 10 draws is 4/5 or 0.80.
Based on this calculation, your answer of 20 draws for the number nine to be chosen is incorrect.
To calculate the chances of drawing two cards with a sum of nine, we need to consider all possible combinations of draws. There are two scenarios in which the sum of nine can be achieved: either both cards are directly numbered as 4 and 5, or they are indirectly numbered, such as 3 and 6, 2 and 7, 1 and 8, or 9 and 0 (assuming 0 is treated as a valid card).
To calculate the probability, we need to determine the number of favorable outcomes (the number of combinations that add up to nine) and the total number of possible outcomes (all possible combinations of draws).
In this case, you are drawing a total of ten times. The order of the draws is not important, so we can calculate the probability using combinations.
Let's break it down:
1. Determine the number of favorable outcomes:
- There are 2 favorable outcomes for a direct combination: drawing 4 and 5.
- There are 4 favorable outcomes for an indirect combination: (3, 6), (2, 7), (1, 8), and (9, 0).
- In total, there are 6 favorable outcomes.
2. Determine the total number of possible outcomes:
- Since you are drawing ten times with replacement, there are a total of 10 x 10 = 100 possible outcomes for each draw.
- Since there are two draws, the total number of possible outcomes is 100 x 100 = 10,000.
3. Calculate the probability:
- The probability is the number of favorable outcomes divided by the total number of possible outcomes.
- In this case, the probability is 6 / 10,000, which simplifies to 0.0006 or 0.06%.
Therefore, your answer of 20 draws for the number nine to be chosen is not correct. The actual probability is estimated to be 0.06%.