Theorem of total probability - class-XI

Question 1 Multiple Choice (Single Answer)

There are 50 marbles of 3 colors: blue yellow and black The probability of picking up a blue marble is 3/10 and that of picking up a yellow marble is 1/2 The probability of picking up a black ball is

1/5
1/10
1/4
4/5

Question 2 Multiple Choice (Single Answer)

Difference between sample space and subset of sample space is considered as

numerical complementary events.
equal compulsory events.
complementary events.
compulsory events.

Question 3 Multiple Choice (Single Answer)

We draw two cards from a deck of shuffled cards without replacement. Find the probability of getting the second card a queen.

$\dfrac{1}{13}$
$\dfrac{2}{13}$
$\dfrac{5}{13}$
None of these

Question 4 Multiple Choice (Single Answer)

Which of the following is true regarding law of total probability?

It is a fundamental rule relating marginal probabilities to conditional probabilities.
It expresses the total probability of an outcome which can be realized via several distinct events
Both are correct
None of these

Question 5 Multiple Choice (Single Answer)

I have three bags that each contain $100$ marbles- Bag $1$ has $75$ red and $25$ blue marbles, Bag $2$ has $60$ red and $40$ blue marbles, Bag $3$ has $45$ red and $55$ blue marbles. I choose one of the bags at random and then pick a marble from the chosen bag, also at random. What is the probability that the chosen marble is red?

$0.60$
$0.40$
$0.50$
None of these

Question 6 Multiple Choice (Single Answer)

For a random experiment, all possible outcomes are called

numerical space.
event space.
sample space.
both b and c.

Question 7 Multiple Choice (Single Answer)

Tossing a coin is an example of .........

Infinite discrete sample space
Finite sample space
Continuous sample space
None of these

Question 8 Multiple Choice (Single Answer)

The term law of total probability is sometimes taken to mean the ____

Law of total expectation
Law of alternatives
Law of variance
None of these

Question 9 Multiple Choice (Single Answer)

The events $E _1, E _2, ........$ represents the partition of the sample space $S$, if they are:

pairwise disjoint
exhaustive
have non-zero probabilities
All are correct

Question 10 Multiple Choice (Single Answer)

The experiment is to repeatedly toss a coin until first tail shows up. Identify the type of the sample space.

Finite sample space
Continuous sample space
Infinite discrete sample space
None of these

$1^{st}$ toss	$2^{nd}$ toss	$3^{rd}$ toss	$4^{th}$ toss	$5^{th}$ toss
$T$	$-$	$-$	$-$	$-$
$H$	$T$	$-$	$-$	$-$
$H$	$H$	$T$	$-$	$-$
$H$	$H$	$H$	$T$	$-$
$H$	$H$	$H$	$H$	$T$

Question 11 Multiple Choice (Single Answer)

The experiment is to randomly select a human and measure his or her length. Identify the type of the sample space.

Finite sample space
Continuous sample space
Infinite discrete sample space
None of these

Question 12 Multiple Choice (Single Answer)

Given a circle of radius $R$, the experiment is to randomly select a chord in that circle. Identify the type of the sample space.

Finite sample space
Continuous sample space
Infinite discrete sample space
None of these

Question 13 Multiple Choice (Single Answer)

Sample space for experiment in which a dice is rolled is

$4$
$8$
$12$
None of these

Question 14 Multiple Choice (Single Answer)

Choosing a birthdate is an example of .........

Infinite discrete sample space
Finite sample space
Continuous sample space
None of these

Question 15 Multiple Choice (Single Answer)

Sample space for experiment in which two coins are tossed is

$8$
$4$
$2$
None of these

Question 16 Multiple Choice (Single Answer)

In a construction job, following are some probabilities given:
Probability that there will be strike is $0.65$, probability that the job will be completed on time if there is no strike is $0.80$, probability that the job will be completed on time if there is strike is $0.32$. Determine probability that the construction job will get complete on time.

$0.438$
$0.538$
$0.488$
None of these

Question 17 Multiple Choice (Single Answer)

There are three boxes, each containing a different number of light bulbs. The first box has 10 bulbs, of which four are dead, the second has six bulbs, of which one is dead, and the third box has eight bulbs of which three are dead. What is the probability of a dead bulb being selected when a bulb is chosen at random from one of the three boxes?

$\dfrac{115}{330}$
$\dfrac{113}{360}$
$\dfrac{113}{330}$
None of these

Question 18 Multiple Choice (Single Answer)

Suppose that two factories supply light bulbs to the market. Factory X's bulbs work for over $5000$ hours in $99%$ of cases, whereas factory Y's bulbs work for over $5000$ hours in $95%$ of cases. It is known that factory X supplies $60%$ of the total bulbs available. What is the chance that a purchased bulb will work for longer than $5000$ hours?

$\dfrac{876}{1000}$
$\dfrac{544}{1000}$
$\dfrac{974}{1000}$
None of these

$1^{st}$ toss	$2^{nd}$ toss	$3^{rd}$ toss	$4^{th}$ toss	$5^{th}$ toss
$T$	$-$	$-$	$-$	$-$
$H$	$T$	$-$	$-$	$-$
$H$	$H$	$T$	$-$	$-$
$H$	$H$	$H$	$T$	$-$
$H$	$H$	$H$	$H$	$T$

$1^{st}$ toss	$2^{nd}$ toss	$3^{rd}$ toss	$4^{th}$ toss	$5^{th}$ toss
$T$	$-$	$-$	$-$	$-$
$H$	$T$	$-$	$-$	$-$
$H$	$H$	$T$	$-$	$-$
$H$	$H$	$H$	$T$	$-$
$H$	$H$	$H$	$H$	$T$

Theorem of total probability - class-XI

Questions

$1^{st}$ toss	$2^{nd}$ toss	$3^{rd}$ toss	$4^{th}$ toss	$5^{th}$ toss
$T$	$-$	$-$	$-$	$-$
$H$	$T$	$-$	$-$	$-$
$H$	$H$	$T$	$-$	$-$
$H$	$H$	$H$	$T$	$-$
$H$	$H$	$H$	$H$	$T$