Free Probability 03 Practice Test - 9th Grade
Question 1
When a coin is tossed, what is the probability of occurrence of "head" as the outcome?
SOLUTION
Solution : D
When you flip a coin, there are two outcomes either head or tail. So the probability of occurrence of the head is the same as the probability of occurrence of the tail that is 12.
Question 2
The range of probability is
-1 to 1 (inclusive)
0 to 1 (inclusive)
1 to 2 (inclusive)
-1 to 0 (inclusive)
SOLUTION
Solution : B
.
Question 3
A coin was tossed 1500 times and out of these, 100 times, the coin stuck somewhere so the result was not counted. The frequency of occurrence of a head was 700. Find the probability of occurrence of a tail.
0.46
0.5
0.3
1
SOLUTION
Solution : B
A coin was tossed 1500 times but 100 times result was not counted.
So, the total number of times result counted = 1400
Number of times head comes = 700
Number of times tail comes = 1400 - 700 = 700
Probability of occurrence of tail =Number of times tail comesTotal number of times result counted
Probability of occurrence of tail =7001400
Probability of occurrence of tail = 0.5
Question 4
Outcome2356Frequency10141620
A dice was thrown 80 times and the frequency of occurrence of 2, 3, 5 and 6 is given in the table. What is the probability of occurrence of 1 or 4?
1
0.67
0.25
14
SOLUTION
Solution : C and D
Total frequency of occurrence of 2, 3, 5 and 6 = 60.
Frequency of occurrence of 1 or 4 = 80 - 60 = 20.
Probability of occurrence of 1 or 4 = Frequency of occurrence of 1 or 4Total number of times die is thrownSo, probability of occurrence of 1 or 4 = 2080 = 14 = 0.25
Question 5
A goldsmith can choose between 3 metals A, B or C to make an artifact. What is the probability that he chooses C?
13
0
1
23
SOLUTION
Solution : A
Since the goldsmith can choose amongst A, B and C, he has 3 possibilities of which the favorable outcome is choosing C. Therefore, probability that he chooses C is 13.
Question 6
BagChocolates112219318422511
5 bags had some amount of chocolates in them, as shown in the table. The probability of occurrence of more than 18 chocolates in a bag if a bag is chosen at random will be
SOLUTION
Solution :Out of the givne 5 bags, bag 2 and bag 4 have more than 18 chocolates.
Probability(E) =number of favorable eventstotal number of events
∴ Probablity of a bag containing more than 18 chocolates =number of bags containing more than 18 chocolatestotal number of bags=25=0.4
Question 7
If an alphabet is picked from the word MISSIMMIPPI what is the probability that an alphabet 'M' is picked?
111
311
811
1
SOLUTION
Solution : B
Total number of alphabets in the word MISSIMMIPPI = 11
Number of times M comes = 3
Probability of picking M = Number of times M comesTotal number of alphabets in the word MISSIMMIPPI
So, probability of its occurrence will be 311.
Question 8
A coin was flipped 100 times. What is the maximum probability of occurrence of tail?
0.5
1
0
0.75
SOLUTION
Solution : B
A coin is tossed 100 times and consider the case when you only get tail 100 times and no head. So, in all the trials you will have a tail.
Probability of getting a tail = Number of times tails appearNumber of times a coin is tossed
Probability of getting a tail = 100100=1
Question 9
What will be the probability that two friends have the same birthday date in a normal year ?
SOLUTION
Solution : B
Number of days in a year = 365
Therefore, total possible outcomes = 365
If they have birthday on same day, then number of favourable outcomes =1
Therefore, required probability =1365
Question 10
A die is rolled twice. Find the probability that 5 will come up both the times.
SOLUTION
Solution : A
Number of all possible outcomes = (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) and (6,6).
The number of all possible outcomes = 36.
There is only one case (5,5) when 5 comes up both the times.
Probability that 5 will come up both the times=Number of times 5 comes up both the timesNumber of all possible outcomes
∴ P (5 will come up both the times) =136