Question

Two cards are drawn brow $52$ cards. Then find the probability that both and
i) both are red
ii) First in an ace and second is a king

Answer 1

Total no. pf cards $=52$

No. of red cards $=26$

No. of aces $=$ No. of kings $=4$

Therefore,

Probability of getting both cards red $=\frac{{}^{26}{C}_2}{{}^{52}{C}_2}=\frac{26\times 25}{52\times 51}=\frac{25}{102}$

Probability of getting first card an ace and second kard a king $=\frac{{}^4{C}_1\times {}^4{C}_1}{{}^{52}{C}_2}=\frac{4\times 4\times 2}{52\times 51}=\frac{8}{663}$