Question

Two cards will be dealt, one at a time and without replacement, from a standard deck of 52 playing cards. In a standard deck, there are 4 Jacks. Answer the following:

a) What is the probability the second card dealt will be a Jack?

P(second card will be Jack) = _______

b) What is the probability both cards dealt will be Jacks?

P(both dealt cards will be Jacks) = _______

c) What is the probability neither card dealt will be a Jack

P(neither dealt card will be a Jack) = ________

d) What is the probability that either card deal is a Jack?

P(either dealt card will be a Jack) = ______

Answer 1

Two cards will be dealt, one at a time and without replacement, from a standard deck of 52 playing cards. In a standard deck, there are 4 jacks.

since, the first card may be anything, so for the second we have 51 cards out of which 4 are jacks.

b) P[Both cards will be Jack]= 4/52*3/51=1/221

for the first card, we have chance of picking a jack with probability 4/52, since we are dealing cards without replacement then for the second card we'll have a chance of probability of picking a second jack with probability of 3/51.

c) If neither card dealt will be a jack, then we have (51-4)=47 options for the first card and 46 options for the second.

P[neither dealt card will be Jack]= 47/52*46/51=1081/1326

d) P(either dealt card will be a Jack) = P[first card will be a jack, second card will not be a jack] + P[first card will not be a jack, second card will be a jack] + P[both cards will be Jack]