Five cards − the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.
(i)What is the probability that the card is the queen?
(ii)If the queen is drawn and put a side, what is the probability that the second card picked up is
(a)an ace?
(b)a queen?
Answers
SOLUTION :
Given : Five cards - ten, jack, queen, king and Ace of diamond are shuffled face downwards
Total number of cards is 5
Total number of outcomes = 5
(i)Let E1 = Event of getting cards which are queen
Number of a Cards which are a queen = 1
Number of outcome favourable to E1 = 1
Probability (E1) = Number of favourable outcomes / Total number of outcomes
P(E1) = 1/5 = 1/5
Hence, the required probability of getting Cards which are queen , P(E1) = 1/5
(ii) Given : If a queen is drawn first and put aside then
Total number of cards is 4
Total number of outcomes = 4
(a) Let E2 = Event of getting ace cards
Number of ace cards = 1
Number of outcome favourable to E2 = 1
Probability (E2) = Number of favourable outcomes / Total number of outcomes
P(E2) = ¼
Hence, the required probability of getting Cards which are ace , P(E2) = 1/4
(b) Let E3 = Event of getting queen cards
Number of queen cards = 0
Number of outcome favourable to E3 = 0
Probability (E3) = Number of favourable outcomes / Total number of outcomes
P(E3) = 0/4 = 0
Hence, the required probability of getting Cards which are queen , P(E3) = 0.
HOPE THIS ANSWER WILL HELP YOU…
Answer:
1/5, 1/4, 0
Step-by-step explanation:
Given, Total number of cards n(S) = 5.
(i) Card is Queen:
Let A be the event of drawing a card which is Queen.
n(A) = 1
Required probability,P(A) = n(A)/n(S)
= 1/5.
If a queen is drawn and put aside, then total number of cards is n(S) = 4
(ii)
(a) an ace:
Let B be the event of drawing a card which is an ace.
n(B) = 1.
Required probability P(B) = n(B)/n(S)
= 1/4
(b) a queen:
Let C be the event of drawing a card which is queen.
n(C) = 0. {As the queen are pus aside}
Required probability P(C) = n(C)/n(S)
= 0.
Hope it helps!