A
What is combined events
Combination of two or more events in an outcome
Write the sample space for the combined events below
Two coins are tossed (H and T representing tails and heads respectively)
{(T,T),(T,H),(H,T),(H,H)}
Write the sample space
Two books are chosen at random from a bookshelf containing two history books (H), a geography book (G) and a mathematis book (M)
{(H1,H2),(H1,G),(H1,M),(H2,H1),(H2,G),(H2,M),(G,H1),(G,H2),(G,M),(M,H1),(M,H2),(M,G)}
A study is carried out on the gender of the children from 16 000 families with two children. Estimate the number of families with at least one son in that study.
12 000
A box contains three yellow pens, five red pens and a black pen. Two pens are chosen at random from the box. Calculate the probability that both pens chosen are of the same colour. (Give answer in fraction form)
13/36
Determine whether the following pairs of events are mutually exclusive events or non-mutually exclusive events
K is the event of selecting a cracked eggs
L is the event of selecting a Grade A egg
Determine whether the following pairs of events are mutually exclusive events or non-mutually exclusive events
P is the event of getting a number that is greater than 4
Q is the event of getting an event number
Non-mutually exclusive
Determine whether the following pairs of events are mutually exclusive events or non-mutually exclusive events
R is the event of selecting a tourist from an European country
S is the event of selecting a tourist from an ASEAN country
Mutually exclusive
Five cards labelled with the letters “C, I, N, T, A” are put in a box.
A card is chosen at random. Calculate the probability that the card chosen is labelled with a consonant or letter “A”. (Give answer in fraction form)
4/5
In a banquet, the probabilities that Zalifah and Maran eat cendol are 5/7 and 3/5 respectively.
Calculate the probability that Zalifah or Maran eats cendol at the banquet. (Give answer in fraction form)
31/35
A fair dice is tossed and then a card is taken out randomly from a box which contains 3 cards labelled “O, N, E”.
Write the sample space for the combine events.
{(1, O), (1, N), (1, E), (2, O), (2, N), (2, E), (3, O), (3, N), (3, E), (4, O), (4, N), (4, E), (5, O), (5, N), (5, E), (6, O), (6, N), (6, E)}
In a reality TV show “I Can See Your Talent”, two participants are selected randomly, one from team A and one team B for a duet. Syak, Mark, Raj and Lee is from team A while Jiha, Shanti dan Mei Hwa is from team B.
State the number of outcomes
n(s)=4 x 3 = 12
SN Café sells 3 types of cakes which are Brownies (B), Congobar (C) and orange cake (O). Two customers want to order a cake and each of them will order one cake.
List down the possible outcomes the order from the first and the second customer.
{(B, B), (B, C), (B, O), (C, B), (C, C), (C, O), (O, B), (O, C), (O, O)}
Two school prefecs will be selected to attend a camp and marching competition where those two programs will be held at the same date and time but in different venue. Four prefects are shortlisted whose are Syam, Wong, Ainul dan Dewi to be selected.
Write the sample space below for the combine events.
{(Syam,Wong),(Syam,Ainul),(Syam,Dewi),(Wong, Syam), (Wong,Ainul),(Wong,Dewi),(Ainul,Syam),(Ainul,Wong),(Ainul,Dewi),(Dewi,Syam),(Dewi,Wong),(Dewi,Ainul)}
n(s)=4x3=12
Two numbers are selected randomly from a set P={x: x is an even number, 1 < x < 10} one by one without replacement.
Write the sample space and state the number of outcomes n(s)
{(2,4),(2,6),(2,8),(4,2),(4,6),(4,8),(6,2),(6,4),),(6,8),(8,2),(8,4),(8,6)}
n(s)=4 x 3 = 12
Identify whether the following combined events below are dependent events or independent events. Justify your answer
A boy chooses two sweets randomly from a jar that consist of 3 lollipops and 5 butter sweets without replacement
Dependent events because the probability of choosing the first sweet affects the probability of getting the second sweet.
Identify whether the following combined events below are dependent events or independent events.
To have the outcome of getting “paper” for two students in a game of “Rock-Scissors-paper”.
Independent events
Identify whether the following combined events below are dependent events or independent events.
Obtain a rose and a black card from a vase that consist of 2 roses and a tulip and then from a box that consist of one white card and 3 black cards.
Independent events because the probability of obtaining a rose does not affects the probability of obtaining a black card.
Calculate the probability of combined events for the independents event below.
A fair dice is tossed and a card is choosen randomly from a box that contains cards labelled with prime number range from number 1 to number 10. Calculate the probability of getting even number for both events. (Give answer in fraction form)
3/6 x 1/4 = 1/8
Calculate the probability of combined events for the independents event below.
Basket A contains 5 watermelons and 7 pineapples while Basket B contains 15 lemons, 14 mangosteens and 3 guavas. A fruit is choosen randomly from Basket A then from Basket B. Calculate the probability of getting a pineapple and a mangosteen. (Give your answer in two significant number).
7/12 x 7/16 = 0.26
Calculate the probability of combined events for the dependents event
Two students are choosen randomly one by one from class 4 Anggun that has 13 male students and 12 female students to answer the questions. Calculate the probability that both of them are male students.(Give answer in fraction form)
13/25 x 12/24 = 13/50
In a group of 36 persons, 9 of them like to eat durian (D), 8 persons like to eat petai (P) and two of them like to eat both. A person is selected randomly.
Calculate the probability that the person is like to eat only durian.
9/36 - 2/36 = 7/36
A brooch is choosen randomly without replacement from a box that has five red brooches, three blue brooches and a green brooch. Then a fair dice is tossed and the outcome is recorded.
(a) If this experiment is carried out 450 times, how many times the factor of 5 be obtained ?
P(Getting factor of 5)
P(M,F)+P(B,F)+P(H,F)
(5/9 x 2/6) + (3/9 x 2/6) + (1/9 x 2/6) = 1/3
1/3 x 450 = 150
The probability of a patient allergics to Pill X is 0.2. Pill X has been given to two patients one person by one person. Draw a tree diagram to show the possible outcomes of the events. Then, calculate the probability that
(a) the first patient is allergic to Pill X.
P (first patient is allergic to Pill X)
P(A,A)+P(A,T)
(0.2 x0.2)+(0.2x0.8)
=0.2
Do you want homework after this class ?
YESSSS!! GIMME ME MOREE