Question

Question #d4d25

Answer 1

`23.5%`

Explanation:

Assuming we are starting with a full deck of 52 cards, the probability of picking a spade the first time is just the ratio of spades to other suits: `13/52 = 25%`. The second selection is the ratio of spades to the remaining deck: `12/51 = 23.5%`

The probability of the second one occurring AFTER the first one is a "conditional probability". It is the product of the two individual probabilities in sequence, divided by the probability of the first event.

If A and B are two events such that given event B has happened and we have to find the probability of event A, then probability of A given B, denoted by P(A/B) is given by

P(A/B) = P(A∩B)/P(B)
where P(A∩B) = P(A)x P(B)

`(0.235 xx 0.25)/0.25 = 0.235 = 23.5%`

http://www.probabilityformula.org/conditional-probability-formula.html