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# Probability Calculations

Probability denotes possibility. To be able to find the probability of a single event to occur, we need to know the total number of possible outcomes first.

Probability is the mathematical measure of how likely an event is to occur. It is the aspect of mathematics that deals with the occurrence of a random event.

Mathematically, probability ranges from 0 to 1, where 0 means it is impossible that the event will occur, and 1 means it is certain the event will occur. In between both values, we have varying degrees of likelihood of the event happening. 0.5 means there is an even chance of the event happening.

When a coin is tossed, for example, there are only two possibilities involved in the outcome. The outcome is either heads or tails. However, when you toss two coins, there are three possible outcomes involved. You either have two heads, two tails, or one head and one tail show up. We will now explore what formula is used to make these calculations, and to help us to solve more complex problems.

## The probability formula

The formula for probability is defined as the possibility of an event happening is equal to the ratio of the number of favourable/desirable outcomes and the total number of outcomes. Mathematically, this is written as:

## Probability calculations

Probability can be written down with the notation below:

Both situations should add up to 1. If event A has a probability between A happening and A not happening, then the probability of event A not happening. For example, if the then.

Assume there was an experiment where a dice was rolled 500 times, and you see 74 fives. The experiential probability of throwing a five is.

Assuming the die is fair, then the theoretical probability of throwing a 5 is.

This is because the 6 is the total possible outcomes there could be from throwing a dice. And 1 indicates the desired outcome (rolling a five).

So on average, if the die is fair, you will see fives.

This mathematics means that by throwing the dice 500 times, provided the dice is fair, you're going to roll approximately 83 fives.

When two coins are tossed simultaneously, what is the probability of getting heads on one coin and tails on the other?

The sample space for when two coins are tossed is as follows;

S = {HH,HT,TH,TT}

Where H= Heads and T= Tails

P(Head on one and Tail on other) = P(HT) + P(TH)

Divide through by 2

This means there is a 50% chance of having a head on one and a tail on another after tossing coins simultaneously.

What is the probability that a random card drawn from a pack of cards is a face card?

Since a standard deck has 52 cards, the total number of outcomes will be 52.

n(S) = 52

Now let E be the event of drawing a face card.

Number of favourable events = n (E)

This can also be expressed in percentages as 23% probability.

We have a box that contains 4 blue balls, 5 red balls, and 11 white balls. If three balls get drawn from the vessel at random, what is the probability that the first ball is red, the second ball is blue, and the third ball is white?

We will first find the probability for each colour picked.

Since there are 20 balls in all, the possible outcome for a pick is 20.

The probability that the first ball will be red then is.

We now have picked a ball which leaves us with the possible outcomes being 19.

So the probability of the second pick being blue is.

Again, because we have another pick already being made, our total possible outcomes reduce by 1, leaving us with 18.

The probability that the third ball is white is.

Therefore the entire probability that the first ball is red, the second ball is blue, and the third ball is white is

P = 0.032

This can also be expressed in percentages as 3.2% probability.

## Probability Calculations - Key takeaways

• Probability is the mathematical measure of how likely an event is to occur.
• Mathematically probability ranges from 0 to 1, where 0 means the event is impossible to occur, and 1 means it is certain the event will occur.
• The probability formula is.
• P (A) is the notation for the probability of event A happening.
• P (A ') is the notation for the probability of event A not happening.
• The probability of an event happening and not happening should both add up to 1.

How to calculate probability: divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring.

How to calculate probability using Venn diagrams: List and group all possible events using set notation. After the listing is done, we use algebra or simple calculations to find the ratios or probabilities.

Probability = Number of favourable outcomes/ Total number of outcomes

How to find the probability of two events: just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.

## Final Probability Calculations Quiz

Question

What is probabilty?

Probability is the mathematical measure of how likely an event is to occur. It is the aspect of mathematics that deals with the occurrence of a random event.

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Question

What is the notation for probability of event A not happening?

P(A')

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Question

What is the notation for probability of event A happening?

P(A)

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Question

How many possible outcomes are there if a coin is tossed?

2

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Question

Both the probability of events happening and they not happening should add up to 1. Is this statement true or false?

True

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Question

What does it mean when the probability of an event happening is 0?

It means there is no probability that such an event will happen

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Question

You pull out a green shirt from a bag of 5 red shirts and 4 green shirts. What is the probability that you will pull out a green shirt again if you do not replace the first one?

1/6

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Question

Jack has an ATM card with a 3-digit pin code - but he has forgotten the numbers! The code can be made of any digit from 0 to 5 and the numbers cannot be repeated. What is the probability that Jack can guess the code correctly?

1/120

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Question

A coach randomly assigns a group of soccer players to Team A (out of 6 boys and 8 girls). The first person picked is a boy. What are the chances the second person on Team A is also a boy?

5/14

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Question

What are compound events?

compound event is an event that has more than one possible outcomes

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Question

Total outcomes you desire to happen is also known as

Favourable outcomes

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Question

What is the probability of flipping a coin and it being Heads?

P(H) = 1/2

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Question

When we throw dice again and again, what are the expected results?

1, 2, 3, 4, 5, 6

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Question

What are the chances of rolling a "4" with a dice?

1/6

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