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SIXTH GRADE / PROBABILITY / TEST 5.1.3

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH.
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

SOME OF OUR QUESTIONS ARE REALLY HARD, FOR THOSE THAT ARE SKILLED IN MATH.
SKIP THEM IN CASE NOT FOR YOU.

IF YOU DESIRE SO, WE CAN DISCUSS HARD/INTERESTING QUESTIONS IN OUR FORUM.

 PROBABILITY
    ♦ 
Sometimes an event depends on very many parameters and some of them are unknown. (Theory of) Probability is our partly sufficient but necessary response to such situations.
    ♦ If we throw a coin in the air we can not control the forces on the coin and do not know if the outcome will be head or tail. But we know if we throw 1000 times 500 of each is to be expected.
    ♦ Experiment, outcome, sample space, event, independent event, discrete/ continuous space are important concepts to be known.
    Ref.-1
    Ref.-2
1. In a ship there are 900 passengers and 750 life jackets. What is the probability for each passenger to reach a life jacket in case of need ?

a) 1
b) 7/8
c) 4/5
d) 5/6
There are of course enough life boats besides jackets .
2. In a small bag there are stones numbered from 1 to 90. What is the probability of drawing a prime numbered stone by the first draw ?

!


a) 25/90
b) 23/90
c) 5/18
d) 3/10
Count the primes in the interval from the figure .
3. During an X-Cup game each team may replace 3 players and have 7 substitutes. The head coach of a team began the game with only 4 substitutes and promised them that he would make use of all 3 permitted changes. What is the probability of entering the game as the second substituter for any of the 3 players ?

!


a) 1/5
b) 1/4
c) 1/3
d) 2/3
Each player has a probability of being the 1st substituter, 3/4. 1-1/4 = 3/4 is to be shared by the remaining 3 .
4. What is the probability of entering the game for each substitute in the previous question ?

a) 1/4
b) 1/2
c) 2/3
d) 3/4
Prevent thinking 1/4 + 1/3 + 1/2 . Its result is 13/12 and the sample şpace is not unque in this line of thinking .
5. Referring to question-3, what is the probability that a substitute who was not the first replacement will be included in the game as the second replacement ?

a) 1/4
b) 1/3
c) 1/2
d) 2/3
The question asked this way means to choose 2 out of 3, sample space changes.
y
6. During an X-Cup game each team may replace 3 players and have 7 substitutes. The head coach of a team began the game with all 7 substitutes and promised them that he would make use of all 3 permitted changes. Which of the followings may not be an element of the sample space in this case ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) {A,C,B}
b) {A,A,B}
c) {C,A,B}
d) {A,B,D}


Associate with each substitute letters from A to G and find 3-element subsets. Have please a look at the ry1 if needed .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. During an X-Cup game each team may replace 3 players and have 7 substitutes. The head coach of a team began the game with all 7 substitutes and promised them that he would make use of all 3 permitted changes and he let the substitute A in. What probability do the rest of the substitutes have to play ?

a) 1/3
b) 2/3
c) 1/2
d) 2/7
Have a look at the ry1 of the previous question, the orange subsets .
8. The below with it's net shown pentagonal trapezohedron is rolled 4 times. What is the probability that the red face will never come down to be the base ?

!


a) 0.1024
b) 0.2048
c) 0.4096
d) 0.8019
The number of red faces are different from the others' .
9. What is the probability that a guy touching the letters section of a keyboard will have touched on only one of the letters of the word "KIZILCAHAMAM" ?

a) 8/26
b) 82/26
c) 8/262
d) (8/26)2
(K,I,Z,L,C,A,H,M) has 8 and total number is 26 .
10. The probability of being the victim of a lightning strike is 1/1 000 000 and the probabilty of death in case of a strike is 10% . How many deaths due to a strike are to be expected in a country with a population of 75 millions ?

!


a) 8
b) 7.5
c) 10
d) 12.5
75 people are expected to be strike victims and ... .
11. What is the probability of being a strike victim within a life span of 80 years if the data of the previous 2 questions are correct ?

!


a) 1/100 000
b) 1/10 000
c) 2/25 000
d) 2/250 000
Just multiply the years and the probability per year .
y
12. In a school, 67% of the students do not like math classes while only 13% of the students do not like both math and arts. What is the probability that a student chosen from the students that do not like math does not like arts either ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) %19
b) %17
c) %20
d) %23
13/67 = ? . For a sample "sample space" have a look at ry1.
13. What is the probability that at least one of them shows a number ≤ 3 if two dices are thrown simultaneously ?

a) 3/4
b) 1/2
c) 2/3
d) 4/5
{1,1},{1,2},{1,3},{1,4},{1,5},{1,6}
{2,1},{2,2},{2,3},{2,4},{2,5},{2,6}
{3,1},{3,2},{3,3},{3,4},{3,5},{3,6}
{4,1},{4,2},{4,3}
,{4,4},{4,5},{4,6}
{5,1},{5,2},{5,3},{5,4},{5,5},{5,6}
{6,1},{6,2},{6,3},{6,4},{6,5},{6,6}
14. What is the probability that one of them is the king of hearts (open card in the figure) if two cards are drawn simultaneously from a deck of 52 of cards ?

!


a) %4
b) %3.8
c) %5.2
d) %3.5


There were 52 and 2 are simultaneously drawn ...
15. From a jar containing 9 black and a white balls 3 balls are drawn consequently without replacement. What is the probability that the 3rd will be the white one ?

a) 1/9
b) 1/5
c) 1/10
d) 2/23
1-1/10= 0.9 ; 0.9 ·(1-1/9) = 0.8 etc. Unless the colors of the first two are not given ...
16. From a jar containing 9 black and a white balls 3 balls are drawn consequently without replacement. What is the probability that the 3rd will be the white one if the first two are black ?

a) 3/23
b) 2/15
c) 1/7
d) 1/8
Just before the 3rd draw the jar contains 7 black and a white balls .
17. Each group of marbles will be put in a different jar having the same group name. Which jar is advantageous if a green marble is desired to be drawn first ?

!


a) d
b) c
c) b
d) a
All groups have the same number of marbles .
y
18. The number of earthquakes of magnitudes 6 to 6.9 , 7 to 7.9 and 8 to 9 from 1994 to 1999 are given in the figure below. Considering that the surface area of Turkey is 1/590 ths of the whole world, in how many years an earthquake of any of these magnitudes are to be expected in Turkey ?

!


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2


a) 2.5
b) 3
c) 3.5
d) 3.3
The sum of the first group gives 831 .
Find the total of all 3 groups. Have a look at ry1 in case of need .
19. Suppose the faces of the figure below are coated as mirrors and it is illuminated from a definite direction with a parallel beam perpendicular to any one of the faces. How many distinct reflections are to be expected ?

!


a) 15
b) 17
c) 11
d) 9
Each mirror will reflect a distinct beam of light.
20. The conditions of the previous question are valid but illumination is direct into the screen. Which of the reflections will be densest ?

a) done by middle-red
b) done by yellow-right
c) done by upper-red
d) done by lower-yellow
The queer ones will reflect with greater beam radius, lower density .
21. The figure turns randomly and swiftly, very swiftly. Which color will the eye see ?

!


a) Yellow
b) Red
c) White
d) Black
Remember prisms or rainbow . just the opposite is here to be observed .
y
22. A regular polyhedral object is illuminated from one direction and the reflected light beams are measured by sensors all around. The result obtained is in the graph given below. How many faces is this object to have ?

!


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) 7
b) 22
c) 24
d) 12


Have please a look at ry1 .
23. Ali and Sharon have put each 3 marbles more into the jar in the figure below as it contains 17 marbles and Ali got one, saw it is not one of hers. What is the probability that Sharon will then draw one that does not belong to her ?

!


a) 2/11 or 3/22
b) 1/11 or 3/23
c) 1/12 or 3/23
d) 1/11 or 3/22
If Ali has drawn one belonging to Sharon, 1/11 otherwise 3/22 .
24. What is the probability of Ali of the previous question to have chosen a marble of Sharon ?

a) 2/23
b) 1/11
c) 3/23
d) 4/47
Draw is made as the jar contains 23 marbles 3 of which belong to Sharon .
25. Which of the choices is the unique answer of question-23 ?

a) %8.5
b) %6.5
c) %13
d) %17
Ali has drawn a marble belonging to Sharon with a probability of 3/23 and not belonging with 20/23 .
[(3/23)·(1/11) + (20/23)·(3/22)] = ?
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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