Math Olympiad Test: Probability- 2 - Class 9 MCQ

Number of red balls = 6
Number of white balls = 8
Number of green balls = 5
Number of black balls = 3
Total number of balls = 6 + 8 + 5 + 3 = 22
P (neither white nor black ball) = P (red or green ball) 

Hence the probability of neither white nor black is 1/2.

Let the number of black balls in the bag be x
∴ 
⇒ x = 15
Hence, there are 15 blue balls in the bag.

P (getting a non–defective bulb)

P (occurrence of a event) + P (non- occurrence of event) = total probability = 1

Number of multiples of 

∴  Required probability 

King, queen and jack are known as face cards
Number of red face cards = 2 × 3 = 6
∴ Required probability = 6/52 = 3/26

The outcomes are:
(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)  (5, 5)  (5, 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)
Even × odd = even and odd × odd = odd. 
∴ For product to be odd, both numbers should be odd. 
∴ Required probability = 9/36 = 1/4.

Probability defines the likelihood of occurrence of an event.
An event whose occurrence is 100% sure, those events are called certain events.
The probability of such an event is always 1.
Example: The probability of getting a number between 1 to 6 when rolling a die is a certain event.
Thus, the probability of an event that is certain to occur is 1.

The probability of getting all tails

P (composite number)

{∵ composite numbers are 4 and 6}

Prime numbers are 2, 3, 5, 7
∴ Sum of frequencies = 23 + 20 + 11 + 30 = 84
∴ Required probability = 84/200 = 42/100 = 0.42

Prime numbers which can get as a sum of the numbers on dice are 2, 3, 5, 7, 11
∴ Required probability 

Total outcomes = 1000
Frequency of Head = 455
Frequency of Tail = 545
Probability of getting head = 455/1000 = 0.455
Probability of getting tail = 545/1000 = 0.545 or 109/200.

No. of cards in pack = 52
P (getting a king)
= 4/52 = 1/13.

Formula: Probability = Number of favorable outcomes/Total number of outcomes
When three coins are tossed then the outcome will be any one of these combinations
(TTT, THT, TTH, THH, HTT, HHT, HTH, HHH)
So, the total number of outcomes is 8
Now, for exactly two heads, the favorable outcome is (THH, HHT, HTH)
We can say that the total number of favorable outcomes is 3
Again, from the formula
Probability = Number of favorable outcomes/Total number of outcomes
Probability = 3/8
∴ The probability of getting exactly two heads is 3/8.