A card is drawn from a well shuffled pack of cards . Find the probability that the card drawn is : (a) a queen (b) a king bearing diamond sign (c) a black card (d) a jack (e) black and a queen (f) either black or queen (g) a red card (h) a face card (i) a diamond or a club (j) neither heart nor a jack (k) a 2 of diamond (l) an ace of hearts (m)a face card of red color (n) 10 of a black “suit”..
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Answers
Answer:
a )1/13
b)1/52
c)3/26
d)1/13
e)1/26
f)7/13
g)3/26
h)3/13
i)3/26
j)9/13
k)1/52
l)1/52
m)3/26
n)1/26
Step-by-step explanation:
Answer:
Given: A card is drawn from a well shuffled pack of cards
To find: Find the probability that the card drawn is in the following.
Step-by-step explanation:
A pack of cards have 52 cards, 26 black and four kinds each of 13 cards from 2 to 10, one ace, one ace, one jack, one queen and one king.
therefore, the Total number of possible events = 52
a) Let Q be the occurrence of favorable event such that it is a queen. Number of events = 4
∴P(Q)=4/52 = 1/13
b)Let A be the occurrence of favorable events such that it is a king bearing diamond sign which can be 1.
∴P(A) = 1/52
c) Let L be the occurrence of favorable event such that it is a black card.
∴ Number events = 26
∴P(L) =26/52 =1/2
d) Let J be the occurrence of favorable events such that it is a jack.
∴Number of events = 4
∴P(J) = 4/52 = 1/13
e) Let C be the occurrence of favorable events such that it is black and a queen which can be 2.
∴P(C) = 2/52 = 1/26
f) Let B be the occurrence of favorable events such that it is either a black card or a queen.
Total = number of black cards = 26 + 2 red queens = 28
∴P(B) = 28/52 = 7/13
g) Let S be the occurence of favourable event such that it is a red card
∴ Number of events = 26
∴P(S)= 26/52 = 1/2
h) Probability of getting a face card = Number of face cards/Total number of outcomes
12/52 = 3/13
i) Let D be the occurence of favourable event such that it is a diamond or a club
So, no, of diamonds= 13 and np. of clubs = 13
∴ Number of events = 26
∴P(D)= 26/52 = 1/2
j) Let E be the event of getting a neither a spade nor a jack.
There are 13 hearts and 3 other jacks. So remaining cards = 52-13-3 = 36
There will be 36 cards which are neither a spade nor a jack.
Number of favorable outcomes = 36
P(E) = 36/52 = 9/13
k) Let C be the occurrence of favorable events such that it is a 2 of diamond which can be 1
∴P(C) = 1/52
l) Let H be the occurrence of favorable event such that it is an ace of hearts
So, no. of total outcomes = 13
∴ Number of events = 1
∴P(H)= 1/13
m) Probability of getting a red face card = Number of red face cards/Total number of outcomes
We will have 3 diamond face cards and 3 heart face cards that sum up to 6 red face cards.
= 6/52 = 3/26
n) Total no. of outcomes =52
No of ways in which ′ 10 ′ of black suit chosen is =2
Probability = 2/52 = 1/26
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