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We think that the probability of drawing a winning pair is 3 / 20 or 15 / 100 or 15% chance.
This is how we solved it:
First we came up with an algebraic sentence to help us figure out the answer.
r x b = n
(r) representing Red Cards (b) Representing Blue Cards (n) Representing a Perfect Square
e.g
r (5) x b (5) = n (25)
By understanding what variables are needed to filled in accordance to the given criteria (multiplying integer by itself), we can easily identify the card "Pairs" in order to figure out its probability.
To figure out how many perfect squares there are in this game, we have the match up the identical integers of each Card Color.
Therefore, there are only 3 possible Winning Pairs/Perfect Squares, 1 , 3 , 5
Also, there are 20 possible combinations. This is because for every RED card pulled out, any ONE of the FOUR different BLUE cards can be pulled out as well.
5 RED x 4 BLUE = 20 CARDS
This makes the probability of drawing a winning pair 3 / 20 or 15 / 100 or 15% chance
Going back to our rule, we can verify if these pairs are correct.
RED BLUE 1 1 , 3 , 4 , 5 = 1 and 1................................................1 x 1 = 1 (1 squared) 3 1 , 3 , 4 , 5 = 3 and 3................................................2 x 2 = 4 (2 squared) 5 1 , 3 , 4 , 5 = 5 and 5................................................5 x 5 = 25 (5 squared) 9 1 , 3 , 4 , 5 = N/A 12 1 , 3 , 4 , 5 = N/A
Actually the probability of a winning pair is 7/20. Here's how we know: In order to determine the probability, we must determine the number of ways to obtain a perfect square and divide it by the total number of possible selections of one red card and one blue card. Of all the combinations, we see that 20 products can be formed. The number 1 is a perfect square, (1 1), and it occurs one time. The number 4 is a perfect square, (2 2), and it occurs one time. The number 9 is a perfect square, (3 3), and it occurs two times. The number 25 is a perfect square, (5 5), and it occurs one time. The number 36 is a perfect square, (6 6), and it occurs two times. Seven of the products are perfect squares. Therefore, the probability of drawing a winning pair is 7/20.
Whoa whoa whoa! Please don't feel embarrassed Jonathan. You and your sis have been all-stars on this forum. My intention was never to embarrass. Continue to be awesome on this blog, take risks and don't fret about right or wrong!
Yello mates
ReplyDeleteOk so this is how I have gotten to this answer.
To get the perfect square you have to multiply by the same number
Red card numbers: 1,3,5,9,12
Blue card numbers: 1,3,4,5
Same between numbers: 1,3,5
1 x 1 = 1 3 x 3 = 9 5 x 5 = 25
Perfect squares: 1, 9, 25
Only 3 combinations to be able to win this game
Total combinations: Alot :P
Naaa its 20 combination in total.
Combinations:
#1. Blue: 1x1 :Red #2. Blue: 1x3 :Red #3. Blue:1x5 :Red #4. Blue: 1x9 :Red #5. Blue:1x12 :Red #6. Blue: 3x1 :Red #7. Blue: 3x3 :Red #8. Blue: 3x5 :Red #9. Blue: 3x9 :Red #10. Blue: 3x12 :Red #11. Blue: 4x1 :Red #12. Blue: 4x3 :Red #13. Blue: 4x5 :Red #14. Blue: 4x9 :Red #15. Blue: 4x12 :Red #16. Blue: 5x1 :Red #17. Blue: 5x3 :Red #18. Blue: 5x5 :Red #19. Blue: 5x9 :Red #20. Blue: 5x12 :Red
Gosh so much typing
Anyways, The probability of winning the game is..
3/20. 15/100
15%
0.15
In any words this game would be very unlikely to get the winning pairs.
That is all
Byeeeee!!! lads :D
Good john
DeleteBut next time read the tittle it says to use algebraic terms.
Kk
Hi my sister and I did this together o:
ReplyDeleteWe think that the probability of drawing a winning pair is 3 / 20 or 15 / 100 or 15% chance.
This is how we solved it:
First we came up with an algebraic sentence to help us figure out the answer.
r x b = n
(r) representing Red Cards
(b) Representing Blue Cards
(n) Representing a Perfect Square
e.g
r (5) x b (5) = n (25)
By understanding what variables are needed to filled in accordance to the given criteria (multiplying integer by itself), we can easily identify the card "Pairs" in order to figure out its probability.
To figure out how many perfect squares there are in this game, we have the match up the identical integers of each Card Color.
Red Blue
1 1 , 3 , 4 , 5 = 1 and 1
3 1 , 3 , 4 , 5 = 3 and 3
5 1 , 3 , 4 , 5 = 5 and 5
9 1 , 3 , 4 , 5 = N/A
12 1 , 3 , 4 , 5 = N/A
Therefore, there are only 3 possible Winning Pairs/Perfect Squares, 1 , 3 , 5
Also, there are 20 possible combinations. This is because for every RED card pulled out, any ONE of the FOUR different BLUE cards can be pulled out as well.
5 RED x 4 BLUE = 20 CARDS
This makes the probability of drawing a winning pair 3 / 20 or 15 / 100 or 15% chance
Going back to our rule, we can verify if these pairs are correct.
RED BLUE
1 1 , 3 , 4 , 5 = 1 and 1................................................1 x 1 = 1 (1 squared)
3 1 , 3 , 4 , 5 = 3 and 3................................................2 x 2 = 4 (2 squared)
5 1 , 3 , 4 , 5 = 5 and 5................................................5 x 5 = 25 (5 squared)
9 1 , 3 , 4 , 5 = N/A
12 1 , 3 , 4 , 5 = N/A
*DING!*
Thanks so much!
I like how you represent the terms/cards algebraically.
DeleteActually the probability of a winning pair is 7/20. Here's how we know:
ReplyDeleteIn order to determine the probability, we must determine the number of ways to obtain a
perfect square and divide it by the total number of possible selections of one red card and one
blue card.
Of all the combinations, we see that 20 products can be formed. The number 1 is a perfect square, (1 1),
and it occurs one time. The number 4 is a perfect square, (2 2), and it occurs one time. The
number 9 is a perfect square, (3 3), and it occurs two times. The number 25 is a perfect
square, (5 5), and it occurs one time. The number 36 is a perfect square, (6 6), and it
occurs two times. Seven of the products are perfect squares. Therefore, the probability of
drawing a winning pair is 7/20.
Wow...embarrassing!
DeleteThanks for the answer Mr.Milette! :)
Whoa whoa whoa! Please don't feel embarrassed Jonathan. You and your sis have been all-stars on this forum. My intention was never to embarrass. Continue to be awesome on this blog, take risks and don't fret about right or wrong!
DeleteLol failed, aleast we tried
Delete