Which of the following pairs of events are independent?
A. Drawing two cards without replacement from a deck: A = first is an ace, B = second is an ace.
B. Rolling a die twice: A = first roll is 5, B = sum is 10.
C. Selecting a student from a class: A = student is male, B = student plays on the football team (all footballers are male).
D. Tossing a fair coin twice: A = first toss is head, B = second toss is tail.
Answer: Option D
Solution (By JKSSB Mock Tests)
Coin tosses are independent. In A, without replacement, not independent. In B, outcome of first affects probability of sum. In D, P(B|A) >0 but P(B|A')=0, so not independent.
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