Question

An MBM applies for a job in two firms X and Y. The probability is being selected in firm X is $0.7$and being rejected at Y is $0.5$. The probability of at least one of his applications being rejected is $0.6$. The probability that he will be selected in one of the firms, is
A. 0.6
B. 0.4
C. 0.8
D. None of these

Answer 1

X And Y are two firms in which an MBM applied probability that may be selected in X is $P(X) = 0.7$ probability that may not be selected in X is $P(\mathop X\limits^ - ) = 1 - 0.7 = 0.3$
Probability that may be selected in Y is $P(Y) = 1 - P(Y)$
$\mathop Y\limits^ -$ denotes he may not be selected.

Complete step by step solution:

P(X) = 0.7\,\,\,\,\,\,\,\,\,P(\mathop X\limits^ - ) = 0.3 \\\ P(\mathop Y\limits^ - ) = 0.5\,\,\,\,\,\,\,\,\,\,\,P(Y) = 0.5 \\\ and\,P(\mathop X\limits^ - \cup \mathop Y\limits^ - ) = 0.6 \\\ \end{gathered} $$ Probability that person will be selected in one of the two firms X or Y is $$\begin{gathered} P(X \cup Y) = 1 - P(\mathop X\limits^ - \cap \mathop Y\limits^ - ) \\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1 - (P(\mathop X\limits^ - ) + P(\mathop Y\limits^ - ) - P(\mathop X\limits^ - \cup \mathop Y\limits^ - ) \\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1 - (0.3 + 0.5 - 0.6) \\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1 - 0.2 = 0.8 \\\ \end{gathered} $$ **Thus, the correct answer is option C.** **Additional Information.** Probability is a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance. Experiment: Any phenomenon like rolling a dice, tossing a coin, drawing a card from a well-shuffled deck, etc. Outcome: The Result of any event; like number appearing on a dice, side of a coin, drawn out card, etc. Sample Space: The set of all possible outcomes. Event: Any combination of possible outcomes or the subset of sample space; like getting an even number on rolled dice, getting a head/tail on a flipped coin, drawing out a king/queen/ace of any suit. Probability Function: A function giving the probability for each outcome **Note:** The solution can be done without using the formula i.e. By using the data Relationally.