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5 B) Working Out Probability - Part 1
5 B) Working Out Probability - Part 1
We are able to work out the probability of an event occurring by using the following formula:
The above formula is for working out the probability as a fraction or decimal. If we want to have the probability as a percentage, we would multiply the formula above by 100.
Example 1 – Dice
Let’s suppose that we have a fair 6-sided dice (fair means that there is an equal chance of the dice landing on each of the side. An unfair dice may be weighted, which would mean that there is a greater chance of the dice landing on a particular side). There are 6 numbers on the dice and therefore 6 possible outcomes, which are 1, 2, 3, 4, 5 and 6. Each of these 6 outcomes are equally likely to occur.
Let’s work out what the probability is that the dice will land on the number 2. To work out the probability, we will be using the following formula:
Let’s suppose that we have a fair 6-sided dice (fair means that there is an equal chance of the dice landing on each of the side. An unfair dice may be weighted, which would mean that there is a greater chance of the dice landing on a particular side). There are 6 numbers on the dice and therefore 6 possible outcomes, which are 1, 2, 3, 4, 5 and 6. Each of these 6 outcomes are equally likely to occur.
Let’s work out what the probability is that the dice will land on the number 2. To work out the probability, we will be using the following formula:
One of the outcomes is a 2 and there are 6 possible outcomes. Therefore, the probability of rolling a 2 from a fair dice is a sixth.
Let’s now suppose that we want to work out what the probability is of rolling the dice and obtaining a number that is greater than 3. There are 3 outcomes that are greater than 3, and these outcomes are 4, 5 and 6. Therefore, the probability is:
When we give the probability of an event occurring in fractions, we need to make sure that we have simplified the fraction (given the fraction in its simplest form). The fraction above can be simplified by dividing the numerator and the denominator by the highest common factor of the numerator and the denominator (the numerator is the number at the top of fraction and the denominator is the number at the bottom of the fraction). The highest common factors between 3 and 6 is 3. Therefore, we divide the numerator and the denominator by 3.
The simplified fraction becomes ½.
Example 2 – Balls
Suppose that we have a bag of balls. There are three different colour balls in the bag; 5 of the balls are green, 3 of the balls are red and 7 of the balls are pink.
What is the probability of the following events occurring?
a) Picking a green ball?
b) Picking a pink ball?
c) Picking a ball that is either green or pink?
d) Picking a white ball?
Part A
To work out the probability of picking a green ball, we divide the number of green balls by the number of balls in the bag. We are told in the question that there are 5 green balls. We are able to work out the number of balls in the bag by adding the number of each of the colours together. When we do this, we find that there are 15 balls (no. green + no. red + no. pink = 5 + 3 + 7 = 15). Therefore, the number of ways that the outcome can occur is 5 and the total number of outcomes is 15. This give us the fraction below:
Suppose that we have a bag of balls. There are three different colour balls in the bag; 5 of the balls are green, 3 of the balls are red and 7 of the balls are pink.
What is the probability of the following events occurring?
a) Picking a green ball?
b) Picking a pink ball?
c) Picking a ball that is either green or pink?
d) Picking a white ball?
Part A
To work out the probability of picking a green ball, we divide the number of green balls by the number of balls in the bag. We are told in the question that there are 5 green balls. We are able to work out the number of balls in the bag by adding the number of each of the colours together. When we do this, we find that there are 15 balls (no. green + no. red + no. pink = 5 + 3 + 7 = 15). Therefore, the number of ways that the outcome can occur is 5 and the total number of outcomes is 15. This give us the fraction below:
We need to remember to simplify our answers. The highest common factor between 5 and 15 is 5, so we divide the numerator and the denominator by 5.
The probability of picking a green ball is 1/3.
Part B
We work out the probability of picking a pink ball by dividing the number of pink balls, which is 7, by the total number of balls in the bag, which is 15. Therefore, the probability of picking a pink ball is:
There are no common factors between the numerator and the denominator in this fraction, which means that the fraction is already in its simplest form.
Part C
We obtain the probability of picking a green or pink ball by adding the number of green and pink balls together (this is to work out the numbers of ways that this event can occur). There are 5 green balls and 7 pink balls, which means that there are 12 green or pink balls. We then divide this number by the number of balls that are in the bag, which is 15. The probability of picking a green or pink ball is:
Part C
We obtain the probability of picking a green or pink ball by adding the number of green and pink balls together (this is to work out the numbers of ways that this event can occur). There are 5 green balls and 7 pink balls, which means that there are 12 green or pink balls. We then divide this number by the number of balls that are in the bag, which is 15. The probability of picking a green or pink ball is:
We now need to check whether our answer can be simplified, which we do by looking for common factors between the numerator and the denominator. This fraction can be simplified because 12 and 15 both have a factor of 3, and this means that we simplify the fraction by dividing the numerator and the denominator by 3.
Part D
The final part of this example asks us to find the probability of picking a white ball from the bag. There are no white balls in the bag; the bag only contains green, red and pink balls. Therefore, the probability of picking out a white ball is 0; it is impossible to pick a white ball out of a bag that does not contain any white balls.
The final part of this example asks us to find the probability of picking a white ball from the bag. There are no white balls in the bag; the bag only contains green, red and pink balls. Therefore, the probability of picking out a white ball is 0; it is impossible to pick a white ball out of a bag that does not contain any white balls.