Let $X$ denote the number of hours you play during a randomly selected day. The probability that $X$ can take values $x$ has the following form, where $c$ is some constant. $\mathrm{P}(\mathrm{X}=\mathrm{x})=\left\{\begin{array}{lll} 0.1, & \text { if } \mathrm{x}=0 \\ \mathrm{cx}, & \text { if } \mathrm{x}=1 \text { or } \mathrm{x}=2 \\ \mathrm{c}(5-\mathrm{x}), & \text { if } \mathrm{x}=3 \text { or } \mathrm{x}=4 \\ 0, & \text { otherwise } \end{array}\right.$ Match List-I with List-II : | List-I | List-II | | --- | --- | | (A) $ c $ | (I) 0.75 | | (B) $ P(X \leq 2) $ | (II) 0.3 | | (C) $ P(X = 2) $ | (III) 0.55 | | (D) $ P(X \geq 2) $ | (IV) 0.15 |

Let X be random variable which assumes $x_1$, $x_2$, $x_3$, $x_4$ such that 2P(X=$x_1$)= 3P(X=$x_2$)=P(X=$x_3$)=5P(X=$x_4$) , then the probability distribution of X is

If A and B are independent events, then which of the following is not true?

A fair coin is tossed 100 times. The probability of getting head an odd number of times is

If $P(A \cap B) = \frac{1}{2}$, $P(A' \cap B') = \frac{1}{3}$, $P(A) = p$ and $P(B) = 2p$, then value of $p$ is

For a random variable x, probability distribution P(x) is given by $P(x) = \frac{k}{6}(3-x), x = 0, 1, 2$, then

Match List-I with List-II

Choose the correct answer from the options given below:

A die is thrown 6 times. If getting an odd number is a success, then the probability of at least 5 successes is