Question

Let the sample space be

Upper S equals StartSet 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 EndSetS={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Suppose the outcomes are equally likely. Compute the probability of the event

Upper E equals StartSet 1 comma 2 comma 4 comma 6 EndSetE={1, 2, 4, 6}.

Answer 1

Concepts and reason

Probability:

The ratio of the number of favorable outcomes to certain event and total number of possible outcomes is called as the probability of an event.

Fundamentals

The probability of an event is defined as,

$\begin{array}{c}\\{\rm{Probability}} = \frac{{{\rm{Number}}\,{\rm{of}}\,{\rm{favorable}}\,{\rm{outcomes}}\,{\rm{for}}\,{\rm{an}}\,{\rm{event}}}}{{{\rm{Total}}\,{\rm{number}}\,{\rm{of}}\,{\rm{outcomes}}}}\\\\ = \frac{{N\left( E \right)}}{{N\left( S \right)}}\\\end{array}$

The objective of the problem is determined below:

From the information given, the sample space be $S = \left\{ {1,2,3,4,5,6,7,8,9,10} \right\}$ . That is, $N\left( S \right) = 10$ , and the outcome $E = \left\{ {1,2,4,6} \right\}$ . That is, $N\left( E \right) = 4$ , by using these values the probability of the event E is obtained.

The probability of the event E is obtained below:

The required probability is,

$\begin{array}{c}\\P\left( E \right) = \frac{4}{{10}}\\\\ = 0.40\\\end{array}$

Ans:

The probability of the event E is 0.40.