Addition of Probabilities

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Addition of Probabilities(Classical Cards Problems)


  • In the word problem , when the word 'either'/'or' is used it provides enough information that the problem is of Addition of Probabilities.
  • Solved Problem.
  • A card is drawn from a deck. Find probability that the card is a Diamond or Club.
  • Solution :
  • Sample space is deck and n(S)=52.Event A is that card is Diamond so n(A)=13,Event B is that card is Club so n(B)=13. As A and B both are completely independent of each other so P(AUB)=P(A)+P(B) => P(AUB)=13/52+13/52=1/4+1/4=2/4=1/2=>P(AUB)=0.5.


Supplementary Problems :
  1. A card is drawn from a deck.Find Probability that card is a face card or a number card.
  2. A card is drawn from a deck.Find Probability that card is a Club or a face card.
  3. A card is drawn from a deck.Find Probability that card is a king or a queen.
  4. A card is drawn from number cards.Find Probability that card reads an even number or an odd number.(Hint:n(S)=36)
  5. A card is drawn from face cards.Find Probability that card is a jack or an Ace.
  6. A card is drawn from number cards.Find Probability that card is a Queen or a Jack.
  7. A card is drawn from Diamonds.Find Probability that card is a face or a number.
  8. A card is drawn from face cards.Find Probability that card is a Spade or A club.
  9. The Probability that Hamza will go tonight to cineplex to watch a movie is '0.3'.The probability that Cineplex is closed tonight is '0.3'.The Probability that Cineplex is open tonight is '0.4'. Can Hamza watch the Movie Tonight?
  10. The probability that it will rain today is '0.6' and it will not rain today is '0.4'.Will it rain tommorrow?
  11. The card of queen is drawn from the Spades.After that a card was drawn from Spades.The probability that this card is a face card or a queen will be ?

Solutions :

  1. Unity.
  2. 25/52.
  3. 2/13.
  4. Unity.
  5. 0.5.
  6. Zero.
  7. Unity.
  8. 0.5.
  9. Yes,It is more Probable that Hamza Succeed in watching movie Tonight.
  10. Can't be predicted because we know nothing about tommorow.
  11. 0.25.

I am Mechatronics and Control Engineer from UET, Lahore. Helping Engineering students gives me pleasure.

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