P(A)

Ex 1 11 cards containing the letters of the word PROBABILITY is put in a box. A card is taken out at random. Find the probability that the card chosen is (a) letter B(b) a vowel(c) a consonant (a) (b) (c)

Ex 2 There are x red balls and 8 yellow balls in bag. A ball is taken at random from the bag. The probability of getting a red ball is. (a) Find the value of x. (b)If y red balls are then added to the box, the probability of getting a yellow ball becomes ½. Find the value of y. Total number of balls = x + 8 Total number of balls = y + 14

A box contains x orange sweets and 7 strawberry sweets. If a sweet is taken at random from the box, the probability of getting an orange sweet is. Find the value of x. Ex 3

MUTUALLY EXCLUSIVE EVENTS The probability of event A or event B occurring / not mutually exclusive The probability of event A and event B mutually exclusive. because P(A or B)

METHOD Find the possible outcomes of each event. Find the possible outcomes of the sample space. Find the probability of each event. Determine if the events are mutually exclusive. Keywords ‘or’ or ‘at least’. Use the Addition Rule of Probability.

INDEPENDENT EVENTS Two events are independent if the fact A occurs does not affect the probability of B occurring. P(A and B)

METHOD Find the probability of each event. Determine if the events are dependent. Use the Multiplication Rule of Probability to calculate of both events.

Ex 4 Two dice, one black and the other is white, are tossed together. Find the probability that (a) an even number appears on the black dice. (b) the sum of the numbers on the two dice is 7. (c) an even number appears on the black dice and the sum of the numbers on the two dice is 7. (d) an even number appears on the black dice or the sum of the numbers on the two dice is WD BD ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

(a) A= events of even number appears on the black dice. (b) B = events with the sum of the numbers on the two dice is 7. (c) an even number appears on the black dice and the sum of the numbers on the two dice is 7.

(d) an even number appears on the black dice or the sum of the numbers on the two dice is 7.

Ex 5 Sarah is asked to write a number from the set { 1, 2, 3, 3,5,6}. Find the probability that she will write (a) the number 3, (b) the number 5, (c) the number 3 or number 5 (a) (b) (c)

Books Price index in 2000 based on 1998 History5 Geography6 English4 Ex 6 The table shows the number of books on a book shelf. Two books are taken from the shelf at random. Find the probability that both books are of the same category.

Ex 7 The probability that Hamid qualifies for the final of a track event is while the probability that Mohan qualifies is. Find the probability that (a) both of them qualify for the final. (b) only one of them qualifies for the final. HAMIDMOHAN

Tree Diagram a method of listing outcomes of an experiment consisting of a series of activities

Tree diagram for the experiment of tossing two coins start H T H H T T

Show the sample space for tossing one penny and rolling one die. (H = heads, T = tails) Solution: By following the different paths in the tree diagram, we can arrive at the sample space. Sample space: { H1, H2, H3, H4, H5, H6,T1, T2, T3, T4, T5, T6 } The probability of each of these outcomes = (1/2)(1/6) = 1/12 Ex 8

A family has three children. How many outcomes are in the sample space that indicates the sex of the children? Assume that the probability of male (M) and the probability of female (F) are each 1/2. Solution: Sample space: { MMM MMF MFM MFF FMM FMF FFM FFF } There are 8 outcomes in the sample space. The probability of each outcome =(1/2)(1/2)(1/2) = 1/8. Ex 9

Short Quiz (MCQ): Question 1: You are at a carnival. One of the carnival games asks you to pick a door and then pick a curtain behind the door. There are 3 doors and 4 curtains behind each door. How many choices are possible for the player? (a) 3 (b) 12 (c) 24 (d) 36 Solution: No. of possible choices = (3)(4) = 12

Question 2: The 4 aces are removed from a deck of cards. A coin is tossed and one of the aces is chosen. What is the probability of getting heads on the coin and the ace of hearts? Draw a tree diagram to illustrate the sample space. (a) 1/2 (b) 1/4 (c) 1/8 (d) 1/16 Solution: P (getting heads on coin and the ace of hearts) = (1/2)(1/4) =1/8

Question 3: There are 3 trails leading to Camp A from your starting position. There are 3 trails from Camp A to Camp B. How many different routes are there from the starting position to Camp B? Draw a tree diagram to illustrate your answer (a) 3 (b) 6 (c) 9 (d) 12 Solution: No. of different routes = (3)(3) = 9

Question 4: A spinner has 4 equally likely regions numbered 1 to 4. The arrow is spun twice. What is the probability that the spinner will land on a 1 on the first spin and on a red region on the second spin? Draw a tree diagram to represent your answer. (a) 1/2 (b) 1/4 (c )1/6 (d) 1/8 Solution: P(1 and red) = (1/4)(1/2) = 1/8

Question 5: There are two identical bottles. One bottle contains 2 green balls and 1 red ball. The other contains 2 red balls. A bottle is selected at random and a single ball is drawn. What is the probability that the ball is red? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3 Solution: P(first bottle, red) = (1/2)(1/3) = 1/6 P(second bottle, red) = (1/2)(1) = 1/2 P(red) = 1/6 + 1/2 = 2/3