A bag has a large number of green, white, yellow, orange and red sweets (5 flavours).
You pick sweets from the bag without looking. If you pick 2 sweets what different combinations of colours can you get?
If you pick 2 sweets how likely are you to pick two of the same colour?
If you pick 6 sweets what is the probability that two are the same colour?
Click here to download the SAME SWEETS worksheet.
Click here to download the Notes for Teachers – Same Sweets Problem
Tagged with: Permutations and combinations • Probability
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the probability that the two colours are the same is 1.
Ntholeng you have not explained how you got that answer.
If you pick 2 sweets, how many different combinations of colours can you get? Draw a picture and count how many different pairs of colours you get. Remember you get a different result if you pick red first then yellow from picking yellow first then red (like children in a family where one is the elder). Call this number T.
If you pick 2 sweets how many combinations are there with the same colour? Call this N.
Then the probability of picking two the same colour is N divided by T.
Can you work it out? Can you see that you don’t get a probability of 1?
In this way T = 25 then N = 5. This means the probability of picking two sweets of the same colour is 5/25. so, the probability that two sweets have the same colour is 1/5.
but if you pick six sweets the probability of having two sweets sharing a colour is 1 because if there are five colours the sixth sweet will have a colour which is the same as one of the five colours.
My grade 6 learners made sketches of different colour combinations,eg,green and green,green and white etc and they came up with 6 different colour combinations,they also saw that they are likely to get 2 sweets of the same colour 4 times.In 6 sweets, the probability getting 2 of the same colour was. 4 out of 6.
There is more work for them to do. Encourage them to look for all the other colour combinations they have not yet found. They should be able to find 25 different colour combinations of which 5 will give two of the same colour.
For the 5 diffent colours the no. of possible outcomes is 25 and the no. of successful outcomes is 5, therefor the probability of picking 2 sweets with the same colour is 5/25.
You can just click the ‘Notes for Teachers’ link and get the answers and some suggestions for how to use this activity in your lessons. These comment boxes are for teachers to discuss good ways of helping their learners to think mathematically and to become confident problem solvers.
We did the problem practical with my gr 7. We used counters as sweets. I gave each group two counters of each colour. I told them to put one piece of each colour in a tin (5 different colours in a tin). Take any one piece of any colour. Take out any colour from the tin and match it with the one out of the tin and record the combination. After finishing that round we went to round 2 with different colour. We repeated the exercise with all five colours, counted the combinations and came up with 25 combinations with one pair of same colour for each colour (five pair out of twenty five).
Toni there is one thing that don’t understand about this quetion.I have read your notes you have said 5/25 = 1/5 so what I want to know where did you get 25 and 1/5 that’s where I get confused please help me.
There are 25 different possible combinations of colours
(Key: G denotes green, W for white, O for orange, Y for yellow and R for red).
GG, GW, GO, GY, GR,
WG, WW, WO, WY, WR,
OG, OW, OO, OY, OR,
YG, YW, YO, YY, YR,
RG, RW, RO, RY, RR.
Exactly 5 of these are 2 sweets of the same colour: GG, WW, OO, YY and RR.
We work out probabilities as fractions.
Probability of a special event =(Number of ways special event can happen)/(Total number of events)
Probability of picking 2 sweets the same colour = 5/25
The fraction 5/25 is equal to the fraction 1/5 and that is also equal to the decimal 0,2 and to the percentage 20%.
I did this problem of sweets with my grade 5 learners and Iwas using coloured chalks as I was not having sweets then we noticed that there are 25 combinations and out of 25 combinations only 5 combinations have the same colour then we divided 5 by 25 and the answer was a fifth
I think if i pick 2 sweets without looking i could have a combination of=25 colours.Then picking 2 sweets of the same colour is=5.If i pick 6 sweets the probability that 2 are the same colour is=1 because out of 5 sweets i have the sixth will have a colour which is the same as any of the fife colours
I tried to do this exercise, but my answer was 5