Characteristics of Axiomatic Approach

Q. 16. A man is known to speak the truth 4 out of 5 times he throws a die and reports that it is a 6 find the probability that it is actually at 6 with the help of tree diagram

Q.

The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a
person getting the right sequence to open the suitcase?

Q.

A combination lock on a suitcase has 3 wheels, each labelled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, what is the probability of a person guessing the right combination ?

Q. If X and Y are two events such that $P\left(X|Y\right)=\frac{1}{2},P\left(Y|X\right)=\frac{1}{3}andP(X\cap Y)=\frac{1}{6}.$ Then, which of the following is/are correct ?

1. $P(X\cup Y)=\frac{2}{3}$
2. X and Y are independent
3. X and Y are not independent
4. $P(X^C\cap Y)=\frac{1}{3}$

Q.

A card is selected from a pack of 52 cards.
(a) How many points are there in the sample space?
(b) Calculate the probability that the card is an ace of spades.
(c) Calculate the probability that the card is (i) an ace (ii) black card.

Q. 29. 2 persons each makes a single throw with a pair of dice. The probability that the throws are unequal is given by ____.

Q.

In throwing a pair of dice, find the probability of getting an odd number on the first die and a total of 7 on both the sides.

1. 

2. 

3. 

4. 

Q. 36. 3 dice, each numbered 1 to 6 are rolled.One die is fair and others are biased so that for each of them a six is twice as likely to occur as any other score.One of the dice is chosen at random and on two throws it shows a six on each occasion. The prob that the die chosen was biased is

Q.

What is the probability that a leap year has 53 sundays ?

Q. 11. consider the experiment of tosssing a coin. if he coin shows head , toss it again, but if it shows tail then throw a dice . find the conditional probability of the event that the die shows a number greater than 4 given that there is at least one tail

Q.

Which of the following are the conditions to be satisfied in the axiomatic approach to probability?

1. For any event E, P(E) $\ge$ 0

2. P(S) = 1

3. For two mutually exclusive events E and F, $P(E\cup F)=P\left(E\right)+P\left(F\right)$

4. For two exhaustive events E and F, $P(E\cup F)=P\left(E\right)+P\left(F\right)$

Q.

A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is
(i) a vowel (ii) an consonant

Q. A and B throw a pair of dice.If A throws 9, find Bs chances of throwing a higher number.

Q. Match the occurrence of the given events with their probabilities, with respect to rolling a single dice.

1. $\frac{1}{2}$
2. $\frac{1}{3}$
3. $\frac{2}{3}$

Q. 47. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a 6. Find the probability that it is actually a 6.

Q. A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and $\frac{1}{2}$, respectively. If the probability that the student is successful, is $\frac{1}{2}$, then

1. $p=1,q=\frac{1}{2}$
2. $p=q=1$
3. $p=q=\frac{1}{2}$
4. $p=1,q=0$

Q.

In a race between Achilles and tortoise, people assigned probability to Achilles winning and tortoise winning. These probability pairs are listed below. How many of these pairs satisfy the axiomatic approach, assuming only two results are tortoise wins and Achilles wins.

1. 

2. 

3. 

4. 

Q.

Which of the following are the conditions to be satisfied in the axiomatic approach to probability?

1. For any event E, P(E) $\ge$ 0

2. P(S) = 1

3. For two mutually exclusive events E and F, $P(E\cup F)=P\left(E\right)+P\left(F\right)$

4. For two exhaustive events E and F, $P(E\cup F)=P\left(E\right)+P\left(F\right)$

Q. In a race between Achilles and tortoise, people assigned probability to Achilles winning and tortoise winning. These probability pairs are listed below. How many of these pairs satisfy the axiomatic approach, assuming only two results are tortoise wins and Achilles wins.

1. $(\frac{1}{2},\frac{1}{2})$
2. $(-\frac{1}{2},1)$
3. $(-\frac{1}{2},\frac{3}{2})$
4. $(1,0)$

Q.

Complete the table for the following events:

Tossing a dice so that the number 5 may come on the top.

Number of total outcomes	Possible outcomes	Probability of each outcome

Q. The probability that a student will pass the final examination in both English and Hindi is $0.5$ and the probability of passing neither is $0.1$. If the probability of passing the English examination is $0.75$, what is the probability of passing the Hindi examination?

Q.

How does the general multiplication rule differ from the special multiplication rule of probability?

Q.

Forrest got a box of chocolate from Jenny. It had n different chocolates. Forrest asked Jenny how many chocolates the box has. Jenny, who is an aspiring data scientist replied, the probability of you getting a KitKat is $\frac{1}{19}$. How many chocolates are there in the box, if each chocolate brand is equally - likely and there is only one chocolate of each brand?

Q. Out of a pack of 52 cards one is lost, from the remainder of the pack , two cards are drawn and are found to be spades .Find the chance that the missing card is a spade ?

1. 11/50
2. 11/49
3. 10/49
4. 10/50

Q.

4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?