Question

A deck of playing cards has 52 cards, of which 13 are diamonds. If you shuffle the deck well and turn over the top 4 cards, one after the other, what's the probability that all 4 are diamonds?

Answer 1

Answer:

The correct solution is "0.002". A further solution is given below.

Explanation:

The given values are:

The total number of playing cards,

= 52 cards

Total number of diamonds,

= 13

Now,

The probability of top four cards will be:

= $P(First \ diamond)\times P(Second \ diamond)\times P(Third \ diamond)\times P(Fourth \ diamond)$On putting the values, we get

= $\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}\times \frac{10}{49}$

= $0.25\times 0.23\times 0.22\times 0.20$

= $0.002$