Question

2.75 Cards are dealt, one at a time, from a standard 52-card deck. a If the first 2 cards are both spades, what is the probability that the next 3 cards are also spades

Answer 1

Answer:

The answer is "0.00842".

Step-by-step explanation:

Due to these cards, a conventional 52-card set is dealt one at a time.

While the first two cards are spades, then it would be expected that we could find the next three cards tents, too.

Let A draw 2 spade cards out of 52 cards. Let B become the occasion to draw 3 spade cards the remaining 50 end cards $(A \cap B)$ was its case where a 52 card spade is chosen $(2+3)=5$.

The number of plots drawn first from 13 regular 52-cerd decks equals number of,$n(A)=\binom{13}{2}$  probability of event $A, PA =\frac{\binom{13}{2}}{\binom{52}{2}}$

Furthermore, the multitude of possibilities we can pull from of the remaining 11 spades of the previous 3 cards is 50-card decks standard, $n (B) = \binom{11}{3}$  then, the probability of event, $B, P(B)=\frac{\binom{11}{3}}{\binom{50}{3}}$

The chances of five cards being drawn (three spades and two spades),

$P(B \cap A)=\frac{\binom{13}{5}}{\binom{52}{5}}$

Then there is the chance that the next three cards will be picked if the first two are both pads, $P(\frac{B}{A})$

$\to P(\frac{B}{A}) \\\\ =\frac{P(B\cap A )}{P(A)}\\\\=\frac{\frac{\frac{13}{5}}{\frac{52}{2}}}{\frac{\frac{13}{2}}{\frac{52}{2}}}\\\\= 0.00842$