Question

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is

• A. > 0.5
• B. 0.5
• C. $\ge$ 0.5
• D. 0

Answer 1

The correct option is C

$\ge$ 0.5

Let X and Y be two events given by

X : A fails in an examination

Y : B fails in an examination

P(A fails) = P(X) = 0.2

P(B fails) = P(Y) = 0.3

Now, P(either A or B fails) = $P(X\cup Y)$

We know that,

\(P(X \cup Y) \geq P(X) + P(Y) = 0.2 + 0.3 = 0.5

$\Rightarrow P(X\cup Y)\ge 0.5$

$\therefore$ P(either A or B fails) $\le$ 0.5

Hence, the correct answer is option (c).