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:

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