A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a heart or diamond. (b) Compute the probability of randomly selecting a heart or diamond or spade. (c) Compute the probability of randomly selecting a ten or spade.
Accepted Solution
A:
Answer:a) 0.5b) 0.75c) 0.307 Step-by-step explanation:We are given the following information in the question:Number of cards in a deck = 52Formula:[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex] a) P(Heart or Diamond) Total number of hearts and diamonds in a deck = 13 + 13 = 26 P( Heart or Diamond) = [tex]\displaystyle\frac{26}{52} = \displaystyle\frac{1}{2} = 0.5[/tex]b) P(Heart or Diamond or Spade) Total number of hearts, diamonds and spades in a deck = 13 + 13 + 13 = 39P( Heart or Diamond or Spades) = [tex]\displaystyle\frac{39}{52} = \displaystyle\frac{3}{4} = 0.75[/tex]c) P(10 or Spades) Total number of spades in a deck = 13 Number of 10 in a deck = 4P( 10 or Spades) = [tex]\displaystyle\frac{13 + 4 -1}{52} = \displaystyle\frac{16}{52} = \displaystyle\frac{4}{13} = 0.307[/tex]