Question

As shown above, a classic deck of cards is made up of 52 cards. Suppose ne card is selected at random and

calculate the following probabilities.
Round solutions to three decimal places, if necessary.
The probability that a 8 of Diamonds is selected is
The probability that a Heart or Spade is selected is
The probability that a number smaller than 7 (counting the ace as a 1) is selected is

Answer 1

Explanation:

a probability is always the ratio of

desired cases / totally possible cases

in our case, where we pull one card out of 52, the totally possible cases are, of course, 52.

now, we need to find the number of desired cases.

8 of diamonds is pulled.

well, that is one specific card. no other card matches this criteria. so, the probability is

1/52 = 0.019230769... ≈ 0.019

heart or spade is selected.

we have 13 cards of heart.

we have 13 cards of spades.

there is no overlap, so, together they are 26.

the probably is then

26/52 = 1/2 = 0.5

number smaller than 7 is pulled.

"smaller than 7" means 1..6.

that means 6 cards of each of the 4 suits = 24 cards.

the probability is then

24/52 = 6/13 = 0.461538462... ≈ 0.462