Multiple choice

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'. Then $A$ and $B$ are independent events.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes = 6. A = {2, 4, 6}, P(A) = 3/6 = 1/2. B = {1, 2, 3}, P(B) = 3/6 = 1/2. A intersect B = {2}, P(A intersect B) = 1/6. Since P(A)*P(B) = 1/4 != 1/6, the events are not independent.

AI explanation

The sample space of the die has 6 outcomes, where event A (an even number) has 3 outcomes and event B (a red number) has 3 outcomes. The intersection of A and B contains only the number 2, so P(A intersection B) is 1/6. Since P(A) multiplied by P(B) is 1/2 multiplied by 1/2, which equals 1/4, it does not equal 1/6. Therefore, the events are not independent, making the statement False.

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