Test: Axiomatic Probability


10 Questions MCQ Test Mathematics For JEE | Test: Axiomatic Probability


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QUESTION: 1

The events when we have no reason to believe that one is more likely to occur than the other is called:

Solution:

Equally Likely Events Events which have the same chance of occurring Probability. Chance that an event will occur. Theoretically for equally likely events, it is the number of ways an event can occur divided by number of outcomes in the sample space.

QUESTION: 2

One card is drawn from a pack of cards, each of the 52 cards being equally likely to be drawn. The probability that the card drawn is red and a queen is:

Solution:

The cards contains 4 Queen from which 2 are black and 2 are red
we need to find the probability that the card drawn is red and a queen is: 2/52
= 1/26

QUESTION: 3

The probability on the basis of observations and collected data is called:

Solution:

The probability on the basis of observations and collected data is called statistical approach of probability.

QUESTION: 4

A bag contains 12 red balls, 10 white balls and 8 green balls. One ball is drawn from the bag, then the probability that the drawn ball is neither red nor green is:

Solution:
QUESTION: 5

A single letter is selected at random from the word PROBABILITY .The probability that it is a vowel is

Solution:
QUESTION: 6

In a simultaneous toss of two coins, the probability of getting no tail is:

Solution:

Sample space = {HH, HT, TH, TT}
n(SS) = 4 
No tail = {HH}
n(No tail) = 1 
P(No tail) = n(No tail) / n(SS
= 1/4   

QUESTION: 7

Two dice are thrown simultaneously. The probability of getting an even number as the sum is:

Solution:

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};{6,6}
Total outcomes = 36
Favorable events : an even number as the sum :{1,1};{1,3};{1,5};{2,2};{2,4};{2,6};{3,1};{3,3};{3,5};{4,2};{4,4};{4,6};{5,1};{5,3}{5,5};{6,2};{6,4};{6,6} =18
 
So, the probability of getting an even number as the sum:
= Favorable events/Total events
= 18/36
 = 1/2

QUESTION: 8

In a lottery 2000 tickets are sold and 50 equal prizes are rewarded. The probability of not getting a prize if you buy 1 ticket is:

Solution:

Since 1 ticket is choosen out of 2000 tickets
n(S) = 2000C1
= (2000!/1!1999!)
= 2000
Now out of 2000 tickets only 50 have a prize
Hence no of tickets not having prize
= 2000 - 50
= 1950
Let A be the event that if we buy 1 ticket it doesnt have a prize
Hence, 1 ticket will be out of 1950 tickets
n(A) = 1950C1
= 1950
Probability not getting a prize if we get one ticket P(A) = n(A)/n(S) 
= 1950/2000

QUESTION: 9

A die is thrown. (i) A: a number less than 7 (ii) B: a number greater than 7 Then, A ∩ B is:

Solution:
QUESTION: 10

What is the sample space for an experiment when a coin is tossed and then a dice is thrown?

Solution:

When a coin is tossed. Head or Tail may occur. Whereby when a die is thrown the numbers from 1 & 6 may occur.
∴ The sample space S={H1T1, H2T2, H3T3, H4T4, H5T5, H6T6}
H represents Head.,  
H1 represents head in coin and 1 in dice
T represents Tail.

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