Using a deck of 52 cards the probability of drawing an Ace i

Using a deck of 52 cards, the probability of drawing an Ace is 4/52 and the probability of drawing a diamond is 13/52. Explain why the probability of drawing either an Ace OR a diamond is NOT 17/52.

Solution

probability of drawing an Ace is 4/52

probability of drawing a diamond is 13/52

Probability of Ace and Diamond 1/52

P( Ace OR a diamond) = P(ace)+P(Diamond) - P(ace & diamond) = 4/52+13/52 - 1/52 = 16/52