Question

max picks two different cards without replacement from a standard $52$-card deck. what is the probability that the cards are of different suits?

Answer 1

The probability that cards are from different suits is $\frac{39}{51}$

Probability of an event E represented by P(E) can be defined as (The number of favorable outcomes )/(Total number of outcomes).

There are 4 suits hearts, diamonds, club and spade in a standard deck of 52 cards.

Each of them has 13 cards each .

So when we pick first card from a single suit

we can pick it in 13 ways , now 12 cards are left.

We can pick the 2nd card from the same suit in 12 different ways .

So to pick 2 cards from a single suit we have 13x12 ways.

to pick 2 card from 4 suits = 4x13x12=624 ways

Total ways of choosing 2 cards from the pack of 52 cards is 52 X 51 =2652

probability that the cards are of same suits=$\frac{624}{2652} =\frac{12}{51}$

probability that the cards are of different suits=$1-\frac{12}{51} =\frac{39}{51}$

Learn more about Probability here brainly.com/question/15263908

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