Question

A card is randomly selected from a pack of 52 cards and the card is not replaced. Then a second card is chosen. Find the probability that
1) both cards are hearts
2) both cards are clubs
3) first card is red and second card is black

Answer 1

Hint:A pack of 52 cards will have 26 black cards and 26 red cards. And a pack of 52 cards will have 13 hearts, 13 clubs, 13 diamonds, 13 spades. Through this information solve each question. Find the probability to solve those questions.

Complete step by step answer:
Let us go through the first question:
1) Probability that both the cards are hearts:
That will be equal to the probability that the first card will be heart multiplied by the probability that the second card is also heart.
The probability that the first card is heart will be (13/52)
As the card is not replaced during the second pick, the total cards that are available to pick the second card will be 51.
So the probability that the second will be a heart is (12/51) as one heart is already picked in the first time.
Probability that both the cards are hearts = $\dfrac{{13}}{{52}} \times \dfrac{{12}}{{51}}$ = (3/51)
Let us go through the first question:
2) Probability that both the cards are clubs:
That will be equal to the probability that the first card will be club multiplied by the probability that the second card is also club.
The probability that the first card is the club will be (13/52)
As the card is not replaced during the second pick, the total cards that are available to pick the second card will be 51.
So the probability that the second will be a club is (12/51) as one club is already picked in the first time.
Probability that both the cards are clubs = $\dfrac{{13}}{{52}} \times \dfrac{{12}}{{51}}$ = (3/51)
Let us go through the third question
3) The probability that first card is red and the second is black
= probability that first card is red × probability the second is black = $\dfrac{{26}}{{52}} \times \dfrac{{26}}{{51}}$ = (26/102)

Note:
 Read the question properly. Do not make calculation mistakes. Do not assume the data in probability related questions. Go through the topics related to packing of cards and also balls to be drawn from bags.