Relative and Expected Frequency

Probability part 2

Probability of An Event

Probability is the likelihood or chance of an event occurring

Probability = the total number of possible outcomes

    OR

   the number of ways of achieving success

Probability Scale

Example ....

Poll

On a probability scale... what is the chances of you will be captured by aliens tonight?

• Impossible

• Unlikely

• Evens

• Likely

• Certain

Poll

On a probability scale... what is the chances of the day after Saturday is Sunday?

• Impossible

• Unlikely

• Evens

• Likely

• Certain

Probability as A Number

Due to the differences in languages, we tend to use numbers on a scale instead of words ...

Probability scale in numbers ...

Probability of An Event

The probability (P) of an event happening is the number of times the chosen outcomes occurs out of the total number of possible outcomes.

 $P=\ \frac{number\ of\ favourable\ outcomes}{total\ number\ of\ outcomes}$ 



You can express probability as a fraction, decimal or percentage

Example 1

A bag contains 5 green balls, 2 red balls, and 4 yellow balls. One ball is taken out at random, what is the probability that it is

a) green

b) red

c) yellow

Example 2

A cash bag contains two 20c coins, four 10c coins, and five 5c coins, three 2c coins, and three 1c coins. Find the probability that 1 coin selected from random is

a) a 10c coin

b) a 2c coin

Open Ended

A bag contains 8 orange balls, 5 green balls, and 4 silver balls. Find the probability that a ball picked out at random is

a) Silver

b) Orange

c) Green

Please provide answers for a), b) and c)

Expected Frequency

A fair dice is rolled 240 times. How many times would you expect it to roll a number > 4?

P=2/6=1/3 --> number greater than 4 is 5 and 6

Expected Frequency = (Probability of success) x (number of trials)

Expected Frequency of scores greater than 4 = 1/3 x 240 = 80

Example

The spinner shown has four equal sectors. How many 3s would you expect in 100 spins.

Open Ended

A bag contains a large number of marbles of which one in five is red. If I randomly select one marble on 200 occasions, how many times would I expect to select a red marble.

Exclusive Events

Mutually Exclusive = CANNOT happen at the same time

Example:

- Turning left and turning right are Mutually Exclusive

- Tossing a coin: H and T are Mutually Exclusive

- Cards: Kings and Aces are Mutually Exclusive

What is NOT Mutually Exclusive

• Turning left and scratching your head can happen at the same time

• Kings and Hearts

Exclusive Events

When 2 events (call them “A” and “B”) are Mutually Exclusive, it is impossible for them to happen together.

P(A and B) = 0

The probability of A and B together equals 0 (impossible)

The probability of something happening is:

1 – (the probability of it not happening)

Example 1

A bag contains a large number of colored balls. The probability of selecting a red ball is 1/5. What is the probability of selecting a ball which is not red?

P_RED = 1/5

P_{Not red} = 1 - 1/5 = 4/5