Question

Learning task 3: A. from a deck of cards you draw 1 card at random find the probability of drawing each of the following
1. A. red card
2. A black card
3. An ace
4. A spade
5. A king of hearts ​

Answer 1

Concept:

The ratio of the number of favourable outcomes to the total number of outcomes of an event is known as probability.

Given:

A deck of cards and need to pick a card.

Find:

The probability of picking a red card, black card, ace, spade and king of hearts.

Solution:

The number of red cards in the deck $= 26$.

The number of black cards in a deck $= 26$.

The number of ace cards in a deck $=4$.

The number of spade cards in a deck $=13$.

The number of kings of heart cards in a deck $=1$.

Total cards in a deck $=52$.

Probability of red cards  $=\frac{26}{52}$.

                                         $=\frac{1}{2}$.                                  

Probability of black cards $=\frac{26}{52}$

                                           $=\frac{1}{2}$.

Probability of ace cards $=\frac{4}{52}$.

                                        $=\frac{1}{13}$.

Probability of spade cards  $=\frac{13}{52}$.

                                             $=\frac{1}{4}$.

Probability of king of hearts $=\frac{1}{52}$.

Answer 2

Probability:

Probability is the ratio of number of favorable outcomes to the total number of outcomes.

Let's solve the given problem.

From a deck of 52 cards if we draw a random card, we should find the probability of drawing

1. A red card

2. A black card

3. An ace

4. A spade

5. A king of hearts.

1. A Red Card

Let's find the probability of drawing red card.

Total number of favorable outcomes for a red card is

$26$

In a deck of 52 cards 26 cards are red and 26 are black.

Total number of outcomes are

$52$

Now,

$probability = 26 \div 52 \\ = 1 \div 2$

Therefore probability of drawing a red card from a deck of 52 cards is

$1 \div 2$

2. A black card:

Let's find the probability of drawing black card.

Total number of favorable outcomes for a black card is

$26$

In a deck of 52 cards 26 cards are red and 26 are black.

Total number of outcomes are

$52$

Now,

$probability = 26 \div 52 \\ = 1 \div 2$

Therefore probability of drawing a black card from a deck of 52 cards is

$1 \div 2$

3. An ace:

In a deck of 52 cards we have 4 ace cards. Each of the ace is from the sets of hearts, diamonds, spades and clubs.

Favorable outcomes to draw an ace card is

$4$

Total number of outcomes are

$52$

Probability is

$4 \div 52 \\ 1 \div 13$

Therefore the probability of drawing an ace card from a deck of 52 cards is

$1 \div 13$

4. A spade:

Out of 52 cards 13 cards are spades.

Therefore favorable outcomes to draw a spade is

$13$

Total number of outcomes are

$52$

Probability is

$13 \div 52 \\ = 1 \div 4$

Therefore the probability of drawing a spade is

$1 \div 4$

5. A king of hearts:

We have only 1 king card in 13 hearts.

Number of favorable outcomes to draw a king of hearts is

$1$

Total number of outcomes are

$52$

Probability is

$1 \div 52$

Therefore the probability of drawing king of hearts from a deck of 52 cards is

$1 \div 52$

#SPJ2