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dalvyx [7]
3 years ago
6

1) Given P(A) = 0.3 and P(B) = 0.5, do the following.

Mathematics
1 answer:
Delicious77 [7]3 years ago
6 0

Answer:

1) a) 0.8

b) 0.6

2) a) 0.08

b) 0.14

Step-by-step explanation:

1) Given

P(A) = 0.3 and P(B) = 0.5

Let us learn about a formula:

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)

(a) If A and B are mutually exclusive i.e. no common thing in the two events.

In other words:

P(A\ and\ B) = P(A \cap B) = 0

Using above formula:

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}

(b)  P(A and B) = 0.2

Using above formula:

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}

*************************************

1) Given

P(A) = 0.4 and P(B) = 0.2

Let us learn about a formula:

P(A\ and\ B) = P(B) \times P(A/B)  for dependent events

P(A\ and\ B) = P(A) \times P(B) for independent events.

(a) If A and B are independent events :

Using the above formula for independent events:

P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}

(b)  P(A / B) = 0.7

Using above formula:

P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}

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