Question

Construct the Tabular Representation and Histogram Representation of the following probability distribution:

1. In a class of 100 students, 80 students passed in all subjects, 10 failed in one subject, 7 failed in two subjects and 3 failed in three subjects. Find the probability distribution of the variable for number of subjects a student from the given class has failed in.

2. The probability of landing on 1 is 0.25. The probability of landing on 2 is 0.75. Let X be the sum of the two spins. Construct a probability distribution for the random variable x.

Answer 1

1.

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 0 & 1 & 2 & 3 \\ \hline p(x) & 0.80 & 0.10 & 0.07 & 0.03 \\ \end{array}$$

2.

$$P(X=2 )=0.25(0.25)=0.0625$$

$$P(X=3 )=0.25(0.75)+0.75(0.25)=0.3750$$

$$P(X=4 )=0.75(0.75)=0.5625$$

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 2 & 3 & 4 \\ \hline p(x) & 0.0625 & 0.3750 & 0.5625\\ \end{array}$$