Check the solution to "The probability of event Ac is 0.4, the..."

Maggenifh

Answered question

2021-11-16

The probability of event

A^{c}

is 0.4, the probability of

{(A U B)}^{c}

is 0.1, and the probability of the intersection of Aand Bis.2. Whats the probability of event 8?

Answer & Explanation

Camem1937

Beginner2021-11-17Added 10 answers

Step 1
Given Data:
The probability of event $A^{c} s : P (A^{c}) = 0. s : P (A^{c}) = 0.4$
The probability of event ${(A \cup B)}^{c} i s : P {(A \cup B)}^{c} = 0.1$
The probability of event $(A \cap B) s : P (A \cap B) = 0. s : P (A \cap B) = 0.2$
The probability of event A is,
$P (A) = 1 — P (A^{c})$
$= 1 - 0.4$
$= 0.6$
Step 2
The probability of event $(A \cup B)$ is,
$P (A \cup B) = 1 - P {(A \cup B)}^{c}$
$= 1 - 0 .1$
$= 0.9$
The probability of event A union Bis,
$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
$0.9 = 0.6 + P (B) - 0.2$
$P (B) = 0.9 - 0.6 + 0.2$
$P (B) = 0.5$
Thus, the probability of event B is 0.5.

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