1. Probability
How to calculate simple probabilities
D. Smith
02/12/2018

2. The probability of an event happening is given by the rule
Probability = Required Event / Total Possible
i.e. The number of required events divided by the total number of possible events
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3. Getting a 4 on a single dice
There is 1 required event – a four
There are 6 possible events
P(4) = 1/6
The answer may be written as a fraction, decimal or percentage
The P says, “The probability of”
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4. The probability of not getting a 4
There are five numbers on the single dice that are not a 4
There are six possible outcomes
So, P(Not getting a 4) = 5/6
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5. It is important that you notice that the two probabilities add together to give 1
The total probabilities of any event have a total of 1
1/6 + 5/6 = 1
Probability of not getting a 4 on a single dice
Probability of getting a 4 on a single dice
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6. The total of all probabilities for an event equal 1
The total of all probabilities for an event equal 1. This important fact can be used to find probabilities.
For example, you are told that the probability of a football team’s results in the next match are:
P(Win) = 0.3
P(Lose) = 0.5
What is the probability of a draw?
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7. Remember the total of all the probabilities is 1
The team must win, lose or draw.
P(Win) + P(Lose) + P(Draw) = 1
P(Draw) = 1
This is 0.5
This is 0.3
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8. To calculate P(Draw) P(Draw) = 1 – (0.3 + 0.5) P(Draw) = 1 – 0.8
P(Win) + P(Lose) + P(Draw) = 1
P(Draw) = 1
P(Draw) = 1 – ( )
P(Draw) = 1 – 0.8
P(Draw) = 0.2
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9. What did you do?
Add together the probabilities that you know and take this number away from one.
You know P(Win) = 0.3 and P(Lose) = 0.5
You know that the total of all the probabilities is 1
So add 0.3 and 0.5 to get 0.8
Then take this away from 1
1 – 0.8 = 0.2
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10. P(Draw) = 0.2
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11. Can I have a date?
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12. Three boys ring Jane and ask her for a date
Jane decides that she will have a date with one of the boys but cannot decide which of the boys to choose.
Jane knows the boys and the probability that she will choose a certain boy is shown below
Name
Dave
Glyn
Sam
Probability
0.1
O.6 ?
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13. What is the probability that she will choose Sam?
Total Probabilities = 1
P(Dave) + P(Glyn) + P(Sam) = 1
P(Sam) = 1
So P(Sam) = 1 – ( )
P(Sam) = 0.3
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14. Mutually Exclusive
Sounds very clever. It means that one event excludes (makes impossible) another event. You cannot get heads and tails at the same time on a coin. You cannot win and lose at the same time. It allows the fact that total probability is one to be used to solve problems
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15. Probability   Expected number of successes = p (success) × number of trials   Example If a dice is rolled 300 times, how many times would you expect to roll a number greater than 4? P (number> 4) = 2/6 = 1/3 Expected number of successes = p (success) × number of trials Expected number of scores greater than 4 = 1/3 × 300 = 100   1230?
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16.   Exercise 1   1. A dice is rolled 510 times – how many times would you expect to roll a) an even number b) a 4 c) a number less than 4?   2. About 1/6 of people have red hair. How many red haired people would you expect to find in a school of 1230?
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17. 3. The probability that Cardiff City F. C win a match is 3/8
  3. The probability that Cardiff City F.C win a match is 3/8. If they play 24 matches, how many would you expect them to win?   4. One in seven sweets in a bag are strawberry flavoured. If there are 490 bags of sweets, how many times would you expect the first sweet chosen to be strawberry flavoured?  
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18. 5. A pack of playing cards are spilt into two piles
5. A pack of playing cards are spilt into two piles. Pile A has all the picture cards and the aces. All the other cards are in Pile B. a) If you pick a card at random from pile A what is the probability that it is the ace of diamonds? b) How many times would you expect to pick a picture card first from Pile A if you picked a card at random 400 times and replaced the card each time? c) How many times would you expect to pick a heart first from Pile B, if you picked a card at random 240 times?   6. If you remove all the picture cards and the hearts from a deck of cards you are left with a pile of cards. If you pick one card at random… a)     What is the probability that you choose the two of spades? b)    What is the probability that the card is a club? c)     If you were to repeat this 390 times, how many times would you expect to pick a red card?
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19. 7. About one in twelve people have allergies to cats
7. About one in twelve people have allergies to cats. If you asked 900 people in the street, how many would you expect to suffer from this allergy?     8. Thomas forgets his homework diary one day a week (Monday-Friday). Over a period of 30 weeks in school, how many days in total would you expect Thomas to forget his homework diary?
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