One person speaks truth in 60% of the cases and another person in 80% of the cases. They are likely to agree in stating the same fact in

If a random variable $X$ has the following probability distribution:

, then

Match List-I with List-II

Choose the correct answer from the options given below:

It is given that 3% of items manufactured by an industry are defective. The probability that a packet of 250 items contains one defective item is: [Given: $e^{-7.5} \approx 0.000553$]

The probability distribution of a ramdom variable $X$ is:

$P(X=x)=\begin{cases}kx^2,& x=1,2,3\\2kx,&x=4,5,6\\0,&\text{otherwise}\end{cases}$ Where $K$ is a constant

Match List-I with List-II

Choose the correct answer from the options given below:

A letter is known to have come either from KOLKATA or TATANAGAR. On the envelope just two consecutive letters TA are visible. The probability that letter has come from TATANAGAR is

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

A random variable X has the following probability distribution

Then the values of 'a' and P(0 < X < 5) respectively are