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Given a standard deck of cards. Find the probability of drawing a 6 or a Diamond.a) Are these mutually exclusive events? Explain.b) Find the probability of drawing a 6 or a Diamond. Show your work!

User Anunaki
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1 Answer

23 votes
23 votes

As we know that,

There are total 52 cards in the deck.

And a deck has 4 types containing 13 cards each.

The types are: spade, club, diamond and hearts.

So, we have an event (A) with total cards = 13

Each card has four types so event (B), that is the number of cards = 4

Now, probability of picking a diamond is p(A) = 13/52 = 1/4

Probability of picking a 6 = 4/52 = 1/13

Now, if you realize that one 6, that is a diamond 6 is common in both the events, that means that p(A and B) /= 0. Hence, these are not mutually exclusive.

Now, The probability in case of nonexclusive events can be calculated as:

P = P(A) + P (B) - P (A and B)

Here, P (A and B) is equal to 1/52 as one card out of 52 is common in both.

Therefore,

P = 1/13 + 1/4 - 1/52

or

P = 4/52 + 13/52 - 1/52

P = 16/52

p = 4/13

Hence, the probability of drawing a 6 or a Diamond is 4/13.

User Davejlin
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