Characteristics of Axiomatic Approach

Q. An insurance company insured $2000$ scooter drivers, $4000$ car drivers, and $6000$ truck drivers. The probability of accidents are $0.01,0.03$ and $0.15$, respectively. One of the insured persons meets with an accident. The probability that he is a scooter driver is $\frac{p}{q}$ then $q-p$ is

Q. A and B play a game where each is asked to select a number from 1 to 25. If the numbers selected by A and B match, both of them win a prize. The probability that they win their third prize on $5^{th}$ game is equal to:

1. $\frac{6.(24{)}^2}{(25{)}^5}$
2. $\frac{6.(21{)}^2}{(25{)}^5}$
3. $\frac{6.(24{)}^2}{(25{)}^4}$
4. $\frac{(24{)}^2}{(25{)}^2}$

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, respectively, $p$, $q$ and $1/2$. if the probability that the student is successful is $1/2$, then $p(1+q)=$

1. $\frac{1}{2}$
2. $1$
3. $\frac{3}{4}$
4. $\frac{3}{2}$

Q. There are 5 students who play guitar in class XI and 8 students who play guitar in class XII. Each class has 50 students. The probability of choosing class XI is $\frac{2}{5}$ and the probability of choosing class XII is $\frac{3}{5}$. A student is chosen and is found to be playing guitar. If the probability that the chosen student is from class XI is p, then the value of 34p is equal to

1. 15
2. 10
3. 20
4. 5

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. $\frac{11}{50}$

2. $\frac{11}{49}$

3. $\frac{10}{49}$

4. $\frac{10}{50}$

Q.

If $A=w_1,w_2\dots ..w_n$, where $w_i$ are the outcomes, then $P\left(A\right)=P\left(w_1\right)+P\left(w_2\right)\dots ..P\left(w_n\right)$

1. True

2. False

Q. In throwing of a fair die, if the probability of the event ‘a number less than or equal to 4 turns up’ is denoted by P(A), then the value of 30P(A) = ___

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.

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. Range of P(E) is (0, 1)
where E is an event and P(E) is the probability of the event

1. False
2. True