Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

If A and B are two events. The probability that at most one of A, B occurs, is

Options:

$1-P (A ∩ B)$

$P(\overline{A})+P(\overline{B})-P(\overline{A}∩\overline{B})$

$P(\overline{A})+P(\overline{B})+P(A ∪ B)-1$

all the above

Correct Answer:

all the above

Explanation:

We have,

Required probability

$=P(\overline{A}∪\overline{B})= P(\overline{A ∪ B})= 1- P (A ∩ B)$

So, alternative (a) is correct.

Again

$P(\overline{A}∪ \overline{B})=P(\overline{A})+P(\overline{B})-P(\overline{A}∩ \overline{B})$ [By add. Theorem]

So, alternative (b) is correct.

Again,

$P(\overline{A}∪ \overline{B})$

$=P(\overline{A})+P(\overline{B})-P(\overline{A}∩ \overline{B})$

$=P(\overline{A})+P(\overline{B}) -P(\overline{A ∪ B})$

$=P(\overline{A})+P(\overline{B}) - \begin{Bmatrix}1- P(A ∪ B) \end{Bmatrix}$

$=P(\overline{A})+P(\overline{B}) + P(A ∪ B)-1$

So, alternative (c) is also correct.