Category: Probability

1. The classical probability method is applied to an experiment that

2. The probability can never be

3. A standard deck of 52 cards is shuffled. What is the probability of choosing the 5 of diamonds,

4. Two events $A$ and $B$ are independent if and only if

5. The joint probability of two independent events $A$ and $B$ is

6. For two mutually exclusive events $A$ and $B$, $P (A) = 0.2$ and $P (B) = 0.4$, then $P(A \cup B)$ is

7. When two coins are tossed the probability of at least one head is

8. $P(A\cap B)=P(A)\cdot P(B)$, then $A$ and $B$ are

9. The probability of an impossible event is always

10. Let $A_1, A_2, \cdots, A_n$ be $n$ events in an event space. If

\begin{align*}
P(A_iA_j) &= P(A_i)P(A_j) \quad for \quad i\ne j\\
P(A_iA_jA_k) &=P(A_i)P(A_j)P(A_k) \quad for \quad i\ne j \ne k\\
\vdots &\\
P(\cap_{i=1}^n A_i) &= \prod_{i=1}^n P(A_i)
\end{align*}

then the events are called

11. Two mutually exclusive events

12. If $P(A \cap B) = 0.12$ and $P(A) = 0.3$, find $P(B)$ where $A$ and $B$ are independent

13. If the events $B_1, B_2, \cdots, B_k$ partition of this sample space $S$ that $P(B_i)\ne 0$ for $i = 1, 2, \cdots, k$)  then for any event $A$ of $S$

14. Two cards are drawn at random from a standard deck of 52 cards, without replacement. What is the probability of drawing a 7 and a king in that order?

15. If $A$ and $B$ are mutually exclusive, then