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  and Given :  A and B be independent events So, we have                                                     We have,                            
  and Given :  A and B be independent events So, we have                                                     
Given,             Also, A and B  are independent events means  .   Also                                                                                
Given,             Also, A and B  are mutually exclusive means .                                                       
Given :                   and For events E and F to be independent , we need                                                                                                                      Hence, E and F are not indepent events.
Total outcomes .  is the event, ‘the number is even,’ Outcomes of A                                         is the event, ‘the number is red’. Outcomes of B                                                                            Also,                           Thus, both the events A and B are not independent.
 A fair coin and an unbiased die are tossed,then total outputs are:                                                                                         A is the event ‘head appears on the coin’ . Total outcomes of A are :                                                                                  B is the event ‘3 on the die’. Total outcomes of B are :                                 ...
Total oranges = 15 Good oranges = 12 Bad oranges = 3   Let   be the probability that first orange is good. The, we have                           Let   be the probability that second orange is good.                        Let   be the probability that third orange is good.                   The probability that a box  will be approved for sale                                                   ...
  Two cards are drawn at random and without replacement from a pack of 52 playing cards.   There are 26 black cards in a pack of 52.   Let   be the probability that first  cards is black. Then, we have                                Let   be the probability that second  cards is black. Then, we have                              The probability that both the cards are black                     ...
     and   Given :     and   are independent events. So we have,       
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