Assume you have a deck of 52 French playing cards and you have taken out all the

Question

Assume you have a deck of 52 French playing cards and you have taken out all the low number cards up to and including eights, so that you are left with 24 cards (9 10 J Q K A).
a) If you pick two cards one after another at random, what is the probability of getting a pair?
b) If you pick three cards one after another at random, what is the probability of getting a three of a kind?
c) If you pick four cards one after another at random, what is the probability of getting a four of a kind?
d) Would your chances have been better or worse had you used the complete deck of 52 cards?

Explanation / Answer

Total cards = 24

a) First card doesn't really matters, so after first card is drawn there are 23 cards left and among those only 3 cards are there which can give us a pair.

So, P(getting a pair) = 3/23
b) Similarly as above, first card doesn't matter, desired second cards are 3 out of 23 and desired third cards are 2 out of 22.

So, P(getting a three of a kind)=(3/23)*(2/22) = 3/253

c) Similarly, first card doesn't matter, desired second cards are 3 out of 23, desired third cards are 2 out of 22, desired fourth card is one out of 21 cards.

P(getting a four of a kind) = (3/23)*(2/22)*(1/21) = 1/1771
d) Chances would have been much worse if there were 52 cards instead of 24 as numerator for each case would have been same while the denominator would have increased.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.