38. The king, the jack and the 10 of spades are lost from a pack of 52 cards
and a card is drawn from the remaining cards after shuffling. Find the
probability of getting a
) red card
(11) black jack
() med king
(iv) 10 of hearts.
Answers
Answer:
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Step-by-step explanation:
The king, the jack and the 10 spades are lost from a pack of 52 cards and a card is drawn from the remaining cards after shuffling.
To find : The probability of getting
(1) red card
(2) black jack
(3) red king
(4) 10 of hearts
Solution :
\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}Probability=
Total number of outcome
Favorable outcome
In a standard deck of 52 cards,
13 diamonds , 13 club , 13 hearts , 13 spade in which 12 face cards
The king, the jack and the 10 spades are lost from a pack of 52 cards
Cards remaining are 52-1-1-10=40
(1) red card
→ If the king and jack is from red card then number of red cards = 24
Favorable outcome = 24
Total number of outcome = 40
Probability of a red card drawn is
\text{Probability}=\frac{24}{40}=\frac{3}{5}Probability=
40
24
=
5
3
→ If the king and jack is not from red card then number of red cards = 26
Favorable outcome = 26
Total number of outcome = 40
Probability of a red card drawn is
\text{Probability}=\frac{26}{40}=\frac{13}{20}Probability=
40
26
=
20
13
(2) black jack
→ If the jack is from black card then number of black cards = 25
Favorable outcome = 25
Total number of outcome = 40
Probability of black jack drawn is
\text{Probability}=\frac{25}{40}=\frac{5}{8}Probability=
40
25
=
8
5
→ If the jack is not from black card then number of black cards = 26
Favorable outcome = 26
Total number of outcome = 40
Probability of black jack drawn is
\text{Probability}=\frac{26}{40}=\frac{13}{20}Probability=
40
26
=
20
13
(3) red king
→ If the king is from red card then number of red cards = 25
Favorable outcome = 25
Total number of outcome = 40
Probability of red king drawn is
\text{Probability}=\frac{25}{40}=\frac{5}{8}Probability=
40
25
=
8
5
→ If the king is not from red card then number of red cards = 26
Favorable outcome = 26
Total number of outcome = 40
Probability of red king drawn is
\text{Probability}=\frac{26}{40}=\frac{13}{20}Probability=
40
26
=
20
13
(4) 10 of hearts
→ If the king and jack is from hearts then number of hearts cards = 8
Favorable outcome = 8
Total number of outcome = 40
Probability of 10 of hearts drawn is
\text{Probability}=\frac{8}{40}=\frac{1}{5}Probability=
40
8
=
5
1
→ If the king and jack is from hearts then number of hearts cards = 10
Favorable outcome = 10
Total number of outcome = 40
Probability of 10 of hearts drawn is
\text{Probability}=\frac{10}{40}=\frac{1}{4}Probability=
40
10
=
4
1