Short Answer TypeA 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?
One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is a spade”
F : “the card drawn is an ace”.
One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is black”,
F : “the card drawn is a king”.
One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is a king or queen”
F : “the card drawn is a queen or jack”.
A coin is tossed thrice. In which of the following cases are the events E and F independent?
E : the first throw results in head”.
F : “the last throw results in tail”.
A coin is tossed thrice. In which of the following cases are the events E and F independent?
E : “the number of heads is two”.
F : “the last throw results in head”.
A coin is tossed thrice. In which of the following cases are the events E and F independent?
E : “the number of heads is odd”.
F : “the number of tails is odd”.
Long Answer Type S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
E = {HHH, TTT}, F = {HHH, HHT, HTH, THH}
and G = {HHT, HTH, THH, HTT, THT, TTH, TTT}
and 
Also, 
and 
and 
∴ the events (E and F) are independent, and the events (E and G) and (F and G) are dependent.
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