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A Die, Whose Faces Are Marked 1, 2, 3 in Red and 4, 5, 6 in Green is Tossed. Let a Be the Event "Number Obtained is Even" and B Be the Event "Number Obtained is Red". Find If a and B Are Independent Events - CBSE (Commerce) Class 12 - Mathematics

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Questions

A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, ‘the number is even,’ and B be the event, ‘the number is red’. Are A and B independent?

Solution 1

S = {1, 2, 3, 4, 5, 6}

Let A : The number is even = {2, 4, 6}

`=> P(A) = 3/6  = 1/2`

B: The number in Red = {1, 2, 3}

`=> P(A) = 3/6 = 1/2`  and A ∩ B = {2}

`=> P(A ∩ B) = 1/6`

So `P(A).P(B) = = 1/2 xx 1/2 = 1/4`

then `P(A).P(B) != P(A nn B)` 

So A and B are not independent

Solution 2

Total number of outcomes = 6

: the event "number obtained is even"

The outcomes in favour of the event A are 2, 4, 6.

Number of outcomes in favour of event A = 3

`:. P(A) = 3/6 = 1/2`

B : the event "number obtained is red"

The outcomes in favour of the event B are 1, 2, 3.

Number of outcomes in favour of event B = 3

`:. P(B) = 3/6 = 1/2`

So,

`P(A) P(B) = 1/2 xx 1/2 = 1/4`

Now 

A ∩ B : the event "number obtained is even and red"

The outcome in favour of the event A ∩ B is 2.

Number of outcomes in favour of event A ∩ B = 1

∴ P(A ∩ B) = `1/6`

Since P(A ∩ B) ≠ P(A)P(B), therefore, the events A and B are not independent events.

  Is there an error in this question or solution?

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Solution A Die, Whose Faces Are Marked 1, 2, 3 in Red and 4, 5, 6 in Green is Tossed. Let a Be the Event "Number Obtained is Even" and B Be the Event "Number Obtained is Red". Find If a and B Are Independent Events Concept: Independent Events.
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