If a card is chosen at random from a deck of 52 cards what i

If a card is chosen at random from a deck of 52 cards, what is the probability that the card is a 7 or a heart? If a card is chosen at random from a deck of 52 cards, what is the probability that the card is a 2 or a 3 and a club at the same time? If a number is chosen from the set {0, 1, 2, 3, 4, 5, 6}, what is the probability that the number is even? If the probability of rolling a 7 is 1/6, what are the odds in favor of rolling a 7?

Solution

1)number of hearts =13, number of 7\'s =4, number of hearts which are 7 =1

probability that card is 7 or a heart =(13+4-1)_/52

probability that card is 7 or a heart =16_/52

probability that card is 7 or a heart =4_/13

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2)number of cards which are 2 and club =1,number of cards which are 3 and club =1

probability that card is 2 or 3 and a club at the sametime =(1+1)_/52

probability that card is 2 or 3 and a club at the sametime =1_/26

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3)in a set {0,1,2,3,4,5,6}

number of number in set =7 , number of even numbers=4, they are (0,2,4,6)

probability that the number is even =4_/7

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4)probability of rolling 7 is 1_/6

probability of not rolling 7 is 1-(1_/6)= 5_/6

odds in favour of rolling a 7 = (1_/6)/(5_/6)

odds in favour of rolling a 7 = 1_/5