Question

Four cards are drawn from a pack of cards. Find the probability that (i) all are diamond (ii) there

is one card of each suit (iii) there are two spades and two hearts.​

Answer 1

Answer:

i) 13/52 = 1/4

ii)not possible

iii) do it yourself

Answer 2

Answer:

Step-by-step explanation:

Four Cards  are drawn from a pack of 52 cards.

Total number of cases = 52C4.

(i) all are diamond

Total no. of diamonds =13.

Favourable no. of cases=13C4

∴ Required probability= P(all are diamonds)

                                  = Fav. no of cases / Total no. of cases

                                  =13C4 / 52C4 = 0.0026410564225

(ii) there  is one card of each suit

Probability of one card of a suit = 13C1

Favourable cases= 13C1 * 13C1 * 13C1 * 13C1 = 4 * 13C1

∴ Required Probability = P( there  is one card of each suit)

                                  = ( 4 * 13C1 )/ 52C4

                                  = 0.0001920768307

(iii) there are two spades and two hearts.​

Probability of two spades = 13C2

Probability of two hearts = 13C2

Favourable no. of cases = 13C2 * 13C2 = 2 * 13C2

∴ Required probability = P( there are two spades and two hearts )

                                   = (2 * 13C2)/52C4

                                   = 0.0005762304921