What is the probability of getting a black card and a king?

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is

(i)    n black king(ii)    either a black card or a king(iii)    black and a king(iv)    a jack, queen or a king(v)    neither a heart nor a king

(vi)    spade or an ace

(vii)    neither an ace nor a king.

Total number of all possible outcomes = 52.i.e.,    n( S) = 52(i) Let A be the favourable outcomes of getting a black king, thenn( A) = 2Therefore,

P(A) = 

(ii) Let B be the favourable outcomes of getting either a black card or a king, then n(B) = 28Therefore,

P(B) = 

(iii) Let C be the favourable outcomes of getting black and a king, then n(C) = 2Therefore,

P(C) = 

(iv) Let D be tine favourable outcomes of getting a jack, queen or a king then n(D) = 12Therefore,

P(D) = 

(v) Let E be the favourable outcomes of getting neither a Heart nor a king, then n(E) = 36Therefore,

P(E) = 

(vi) Let F be the favourable outcomes of getting spade or an ace, thenn(F) = 16Therefore,

P(F) = 

(vii) Let G be the favourable outcomes of getting neither an ace nor a king, then n(G) = 44Therefore,

P(G) = 

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FORMULA USED:

Probability of an event = Number of favorable outcomes/total number of outcomes

CALCULATION:

Probability of king = 4/52

Probability of black ace = 2/52

Required probability = 4/52 + 2/52 =6/52 = 3/26

∴ Probability is 3/26

• In case of 'or' addition of two probabilities is done.
• There are 4 kings and two black aces in a deck of cards.

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