Answer to Question #245428 in Statistics and Probability for very

Question

Three cards are drawn in succession, without replacement (kartu tidak dikembalikan lagi), from an ordinary deck

of playing cards.

Find the probability that the event A1 ∩ A2 ∩ A3 occurs, where A1 is the event that the first card is a red ace, A2

is the event that the second card is a 10 or a jack, A3 is the event that the third card is greater than 3 but less

than 7.

Answer 1

Let $B=A1⋂A2⋂A3$

Then B means: first card-red ace, second card-10 or jack, third card-4,5 or 6

$P(A1) = {\frac 2 {52}} = {\frac 1 {26}}$

Now deck contains 51 cards(without one red ace)

$P(A2) = {\frac 8 {51}}$

Now deck contains 50 cards(without one red ace and one 10 or jack)

$P(A3) = {\frac {12} {50}} = {\frac 6 {25}}$

Those probabilities were calculated considering previous ones, so:

$P(B) = P(A1)*P(A2)*P(A3) = {\frac 1 {26}} * {\frac 8 {51}}*{\frac 6 {25}} = {\frac {48} {45900}} = {\frac 4 {3825}}$