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Home » A die marked in red and in green is tossed. Let be the event, ‘the number is even,’ and be the event, ‘the number is red’. Are A and B independent?
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 \mathrm{B} be the event, ‘the number is red’. Are A and B independent?
CBSE | Maths | NCERT | Probability
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 \mathrm{B} be the event, ‘the number is red’. Are A and B independent?

Solution:

The dice sample space will be be S={1,2,3,4,5,6}

Let A be the event, the number is even, sample space of the event:

\Rightarrow \mathrm{A}={2,4,6}

\Rightarrow P(A)=3 / 6=1 / 2

Now, Let \mathrm{B} be the event, the number is red, sample space of event B,

\Rightarrow B={1,2,3}

\Rightarrow P(B)=3 / 6=1 / 2

As, A \cap B={2}

\Rightarrow P(A \cap B)=1 / 6 \ldots \ldots . .

And P (A). P(B)=1 / 2 \times 1 / 2=1 / 4 \ldots . . (2)

From (1) and (2) P(A \cap B) \neq P(A) . P(B)

Therefore, A and B are not independent events.

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