Topic 5: Indices with Exercises

What is Probability?
How likely something is to happen.

Definition:
The probability of an event is the measure of the chance that the event will occur as a result of an experiment. The probability of an event A is the number of ways event A can occur divided by the total number of possible outcomes.

Tossing a coin

When  a coin is tossed, there are two possible outcomes:

• Head (H) or
• Tails (T)

We say that the probability of the coin landing H is 1/2.
And the probability of the coin landing T is 1/2.






Throwing a dice

When a single die is thrown, there are six possible outcomes: 1,2,3,4,5,6.

The probability of any one of them is 1/6.



In general probability

Probability of an event happening=Number of ways it can happenTotal number of outcomes

Example: the chances of rolling a "4" with a die

Number of ways it can happen: 1 (there is only 1 face with a "4" on it)

Total number of outcomes: 6 (there are 6 faces altogether)

So the probability = 16

Example: there are 5 marbles in a bag: 4 are blue, and 1 is red. What is the probability that a blue marble gets picked?

Number of ways it can happen: 4 (there are 4 blues)

Total number of outcomes: 5 (there are 5 marbles in total)

So the probability = 45 = 0.8

Example 1:	A spinner has 4 equal sectors colored yellow, blue, green and red. After spinning the spinner, what is the probability of landing on each color?
Outcomes:	The possible outcomes of this experiment are yellow, blue, green, and red.
Probabilities:	P(yellow)  =  # of ways to land on yellow  =  1 total # of colors  4  P(blue)  =  # of ways to land on blue  =  1 total # of colors  4  P(green)  =  # of ways to land on green  =  1 total # of colors  4  P(red)  =  # of ways to land on red  =  1 total # of colors  4  Example 2:  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 The outcomes 1, 2, 3, 4 and 5 are equally likely to occur as a result of this experiment. However, the events even and odd are not equally likely to occur, since there are 3 odd numbers and only 2 even numbers from 1 to 5. Example 3:   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? Outcomes:   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 The outcomes in this experiment are not equally likely to occur. You are more likely to choose a blue marble than any other color. You are least likely to choose a yellow marble. Here are the video of the Probability: -EXERCISE- !GOOD LUCK! Question 1:  A dice is thrown once. What is the probability that the score is a factor 6? a) 1/6 b) 1/2 c) 2/3 d) 1 Question 2: The diagram shows a spinner made up of a piece of card in the shape of a regular pentagon, with a toothpick pushed through its center. The five triangles are numbered from 1 to 5. The spinner is spun until it lands on one of five edges of the pentagon. What is the probability that the number it lands on is odd?  a) 1/5 b) 2/5 c) 1/2 d) 3/5 Question 3: A card is chosen at random from a deck of 52 playing cards. There are 4  Queens and 4 Kings in a deck of playing cards. What is the probability the card chosen is a Queen or  a King? a) 1/13 b) 2/13 c) 1/8 d) 2/11