Introduction to Probability

Q. Alex and his family members stopped at a highway restaurant for a meal. Alex ordered a burger, french fires, and a soft drink. P ordered garlic bread, pizza, and a soft drink. Q ordered garlic bread, french fries, and a soft drink. R ordered the same meal as Alex, while S ordered garlic bread, burger, and a soft drink.​
Which food was ordered by the least number of people?

Q. What is the probability of getting a prime number when a die is rolled ?

1. 1/3
2. 1/2
3. 1/4
4. 3/4

Q. A and B appeared for an interview for two posts. The probability of A's rejection is $\frac{2}{5}$ and that of B's selection is $\frac{4}{7}$. The probability that one of them is selected, is

1. $\frac{17}{35}$
2. $\frac{16}{35}$
3. $\frac{18}{35}$
4. None of these

Q. Assertion :A and B are two candidates seeking in D.C. E. The probability that A is selected is 0.40 & the probability that both A and B are selected is 0.20. Then the probability of B's selection is 0.60. Reason: If $E_1$ and $E_2$ are the events of selection of A and B respectively, then $P(E_1\cap E_2)=P\left(E_1\right)P\left(E_2\right)$.

1. Both Assertion and Reason are individually true and Reason is correct explanation of Assertion
2. Both Assertion and Reason are individually true but Reason is not the correct (proper) explanation of Assertion
3. Assertion is true but Reason is false
4. Assertion is false but Reason is true