Respuesta :
the probability of the next card being 3 is a 4/5 chance
General Idea:
If A and B are independent, then the probability that events A and B both occur is:
[tex] p(A\; and\; B) = p(A) \times p(B). [/tex]
In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B
Applying the concept:
Five cards are drawn from a standard deck of cards. Each card is replaced after being drawn.
There are four 3's in a deck of card, four 2's in a deck of card. In a deck of card there are 52, so...
[tex] \\[tex] p(3\; and\; 3\; and\; 3 \; and \; 2 \; and\; 2)=\frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \\ \\ Multiply \; numerator \; with \; numerator \; and \; denominator \; with \; denominator\\ \\ \frac{4 \cdot 4 \cdot 4 \cdot 4 \cdot 4}{52 \cdot 52 \cdot 52 \cdot 52 \cdot 52} \\ \\ Cancel \; Common\; Factor\\ \\ \frac{1 \cdot 1 \cdot 1 \cdot 1 \cdot 1}{13 \cdot 13 \cdot 13 \cdot 13 \cdot 13} =\frac{1}{13^5} =\frac{1}{371293} [/tex] \; =\; p(3) \times \; p(3) \times \; p(3) \times \; p(2) \times p(2) [/tex]
