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PROBABILITY
1. What is the probability of1.1 getting heads when you throw a coin?
1.2 throwing a 1 on a dice?
HEADS TAILS
2
1
1 2 3 4 5 6
6
1
2. If I have 7 balloons at a party, 4 red and 3 yellow, and a blindfolded person has
to pop one, what is the probability that it will be a red one?
1 2 3 4 5 6 7
7
4
3. If there are 10 balloons at another party, 4 red, 3 yellowwhat are the chances that a red one will be popped first?
1 2 3 4 5 6 7
10
4
and 3 green,
8 9 10
4. At the heart, a box of smarties breaks open and 12 smarties fall on the floor,
(2 red, 3 green, 4 purple, 3 yellow). Mr Loubser is happy to eat off the floor, so he grabs for a smartie (as do a couple of other people who are also happy to eat off the floor).
What is the probability that the first one that is picked up is(i) red?(ii) purple?
12
2 4
5. I have 7 Chinese checkers.
Now for the PROBABILITY TREE:
4 red and 3 blue in a box.a. If I take one out, what is the probability of it being red?
R B4/7 3/7
b. If I take two out, what is the probability of BOTH being red?
R B3/6 3/6
3/6 x 4/7 = 12/42 = 2/7c. If I take two out, what is the probability of one red and one blue?
One red :
Two red :
3/6 x 4/7 = 12/42 = 2/7First red then blue :
R B4/6 2/6
The complete tree looks like:
RB3/6 x 4/7
12/42
RR3/6 x 4/712/42
BR4/6 x 3/7
12/42
BB2/6 x 3/7
6/42
4
7
4/7
3
6
3
6
4/6 x 3/7 = 12/42 = 2/7or first blue then red : Can be: first red then blue or first blue then red
Probability = 2/7 + 2/7 = 4/7
5/10
6. There is a lucky draw, based on the colour of the ticket you draw out of a box (Of course, the box is see through when you draw it. You get R50 if you draw a yellow ticket and R100 if you draw a green one).
In the box are 6 yellow ticketsand 5 green tickets.6.1 If you are allowed to take only 1 ticket, what is the probability of you
drawing a green ticket?
Y G6/11 5/11
Y G6/10 4/10
6.2 If you are allowed to take only two tickets from the box, what is the probability: (NB draw a tree diagram)
a. of drawing 2 green tickets?4/10 x 5/11 = 20/110 = 2/11Two
green : b. of drawing 1 yellow and 1 green ticket?
5/10 x 6/11 = 30/110 = 3/11Yellow then green :
Y G5/10
5/11
5/10 x 6/1130/110
YY5/10 x 6/11
30/110
6/10 x 5/11
30/110
4/10 x 5/11
20/110
The complete tree looks like: YG GY GG
6/10 x 5/11 = 30/110 = 3/11Or green then yellow :
One green :
Can be: first yellow then green or first green then yellowProbability = 3/11 + 3/11 = 6/11
7. There are 9 buttons in a box. 3 red, 4 white and 2 blue.Draw a tree diagram to determine the following:
a. What is the probability of taking a white button?b. If you are allowed to take 2 buttons, what is the
probability of their both being white?c. If you are allowed to take 2 buttons, what is the
probability of their being 2 different colours?
8. There are 12 cards in a pack, 4 jacks, 4 queens and 4 kings.
a. If you pick a card, what is the probability of picking a queen?
b. If you pick a second card, what is the probability of their both being queens? (Do a tree diagram)