Two cards are drawn at random from a pack of 52 cards. Then find the probability of getting one red face card and one black ace?
Answers
Answer:
3/676
Step-by-step explanation:
1) Since, the two cards are drawn simultaneously, the outcome of first will not affect outcome of second.
2) Case 1 : red face card
Total red face cards in deck are :- 6
Total possible cards in the deck are :- 52.
Probability of getting a red face card would be = 6/52 = 3/26
3) Case 2 : One black ace
Total black ace in the deck are : 2
Total possible cards in the deck are :- 52.
Probability of getting a black ace card would be = 2/52 = 1/26
4) Overall probability would be : 3/26 * 1/26 = 3/ 676
Probability of getting one red face card and one black ace is 2 /221
≈ 0.009
Given : Two cards are drawn at random from a pack of 52 cards.
To find : the probability of getting one red face card and one black ace
Solution:
Understand first , what all cards are there in a pack of 52 cards :
Four types : Club , Spade , Diamond & Heart
(Clubs & Spade are black in color. Diamond & heart are Red in color)
Each type has 13 cards :
Ace – (number 1)
Numbered card 2-10
Face Card – Jack (11) , Queen (12) King (13)
2 Cards out of 52 can be drawn in ⁵²C₂ ways
red face card = 6
one red face card can be selected in 6 ways
Black ace = 2
one black ace can be selected in 2 ways
Probability of an event = n(E)/n(S)
n(E) = number of possible outcome of event
n(S) = number of possible sample space outcome
Probability of getting one red face card and one black ace
= ( 6 * 2) / ⁵²C₂
= 12 * 2 / (52 * 51)
= 2/ ( 13 * 17)
= 2 /221
≈ 0.009
Probability of getting one red face card and one black ace is 2 /221
≈ 0.009
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