A fair six–faced die is thrown once and a fair coin is tossed simultaneously
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A fair six–faced die is thrown once and a fair coin is tossed simultaneously. Let
E be the event “the die shows an even number” and F be the event “the coin shows Heads.”
(i) Calculate P(E), P(F) and P(E∩F).
(ii) Decide whether the events E and F are independent. Show all working.
(iii) If the coin is replaced by another coin that shows Heads with probability 0.7 while the die remains fair, state with reason whether E and F would still be independent.