TOPIC 7 : PROBABILITY

Probability is the likelihood of something happening. When someone tells you the probability of something happening, they are telling you how likely that something is. When people buy lottery tickets, the probability of winning is usually stated, and sometimes, it can be something like 1/10,000,000 (or even worse). This tells you that it is not very likely that you will win.

EXAMPLES

A spinner has 4 equal sectors colored yellow, blue, green and red. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red?

SOLUTION : the chances of landing on blue are 1 in 4, or one fourth

                        the chances of landing on red are 1 in 4, or one fourth

A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a yellow marble? Outcome :The possible outcomes of this experiment are red, green, blue and yellow. Probabilities:  P(red)  =  # of ways to choose red  =   6   =   3  total # of marbles 22 11 P(green)  =  # of ways to choose green  =   5  total # of marbles 22 P(blue)  =  # of ways to choose blue  =   8   =   4  total # of marbles 22 11 P(yellow)  =  # of ways to choose yellow  =   3  total # of marbles 22

Choose a number at random from 1 to 5. What is the probability of each outcome? What is the probability that the number chosen is even? What is the probability that the number chosen is odd?

Outcomes:

The possible outcomes of this experiment are 1, 2, 3, 4 and 5 Probabilities:   P(1)  =  # of ways to choose a 1  =  1 total # of numbers 5 P(2)  =  # of ways to choose a 2  =  1 total # of numbers 5 P(3)  =  # of ways to choose a 3  =  1 total # of numbers 5 P(4)  =  # of ways to choose a 4  =  1 total # of numbers 5 P(5)  =  # of ways to choose a 5  =  1 total # of numbers 5 P(even)  =  # of ways to choose an even number  =  2 total # of numbers 5 P(odd)  =  # of ways to choose an odd number  =  3 total # of numbers 5

WATCH THIS VIDEO🔔

PROBABILITY TREE DIAGRAM

Calculating probabilities can be hard, sometimes we add them, sometimes we multiply them, and often it is hard to figure out what to do ... tree diagrams to the rescue!

Here is a tree diagram for the toss of a coin:

There are two "branches" (Heads and Tails) The probability of each branch is written on the branch The outcome is written at the end of the branch

We can extend the tree diagram to two tosses of a coin:

 ANSWER THIS QUESTIONS 😃

1. A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond.

2.  The blood groups of 200 people is distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?

3. A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag.

a) Construct a probability tree of the problem.
b) Calculate the probability that Paul picks:
i) two black balls
ii) a black ball in his second draw