Probability Distribution

Q.

A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card.

Q.

The probability that the same number appears on throwing three dice simultaneously is

1. $\frac{1}{36}$

2. $\frac{5}{36}$

3. $\frac{1}{6}$

4. $\frac{4}{13}$

Q.

A coin is tossed 4 times. The probability that at least one head turns up is

1. $\frac{1}{16}$

2. $\frac{2}{16}$

3. $\frac{14}{16}$

4. $\frac{15}{16}$

Q. 9. An integer is selected between 1-100. Find the probability that it is diviisble by 8

Q. A person throws two fair dice. He wins Rs. $15$ for throwing a doublet (same numbers on the two dice), wins Rs. $12$ when the throw results in the sum of $9$, and loses Rs. $6$ for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :

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

Q. 16. A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is

Q. A random variable $X$ has the following probability distribution:
$$\begin{array}{cccccc}X& 1& 2& 3& 4& 5\\ P\left(X\right)& K^2& 2K& K& 2K& 5K^2\end{array}$$
Then $P(X>2)$ is equal to:

1. $\frac{7}{12}$
2. $\frac{23}{36}$
3. $\frac{1}{36}$
4. $\frac{1}{6}$

Q. An unbalanced dice (with six faces numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90$% of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than $3$ is $0.75$, then the probability that the face value exceeds $3$ is

1. $\frac{80}{171}$
2. $\frac{29}{57}$
3. $\frac{9}{19}$
4. $\frac{82}{171}$

Q. A bag contains $30$ white balls and $10$ red balls. $16$ are drawn one by one randomly from the bag with replacement. If $X$ be the number of white balls drawn, then $\left(\frac{\text{mean of X}}{\text{standard deviation of X}}\right)$ is equal to :

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

Q. A random variable $X$ has probability distribution

$\begin{array}{ccccccccc}X& 1& 2& 3& 4& 5& 6& 7& 8\\ P\left(X\right)& 0.13& 0.22& 0.12& 0.21& 0.13& 0.08& 0.06& 0.05\end{array}$

If events are $E=\left\{x\text{is an odd number}\right\},$$F=\left\{x\text{is divisible by}3\right\}$ and $G=\left\{x\text{is less than}7\right\}$, then the value of $P(E\cup (F\cap G\left)\right)$ is

1. $0.87$
2. $0.77$
3. $0.52$
4. $0.82$