You are drawing one card from a shuffled deck. Let event A be "drawing a spade" and event B be "drawing a face card". You are drawing one card from a shuffled deck of 52 cards. Let event A be "drawing a spade" and event B be "drawing a face card". There are 12 face cards in a deck, of which 3 are spades. Calculate P(A | B).

Step-by-step explanation:

Conditional Probability

It's the probability that a given event A occurs, knowing another event B has occurred. It's written as P(A|B) and is calculated by the formula

Let the event A=Drawing a spade and event B= Drawing a face card

Let's first compute P(B). There are 12 face cards in a deck, thus

To compute we use the fact that there are 3 spades out of the 12 face cards, thus

Finally

The required probability is 1/4 or 0.25

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: