Answer:
1) a) 0.8
b) 0.6
2) a) 0.08
b) 0.14
Step-by-step explanation:
1) Given
[tex]P(A) = 0.3[/tex] and [tex]P(B) = 0.5[/tex]
Let us learn about a formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)[/tex]
(a) If A and B are mutually exclusive i.e. no common thing in the two events.
In other words:
[tex]P(A\ and\ B)[/tex] = [tex]P(A \cap B)[/tex] = 0
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}[/tex]
(b) P(A and B) = 0.2
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}[/tex]
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1) Given
[tex]P(A) = 0.4[/tex] and [tex]P(B) = 0.2[/tex]
Let us learn about a formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B)[/tex] for dependent events
[tex]P(A\ and\ B) = P(A) \times P(B)[/tex] for independent events.
(a) If A and B are independent events :
Using the above formula for independent events:
[tex]P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}[/tex]
(b) [tex]P(A / B) = 0.7[/tex]
Using above formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}[/tex]
