Question

rulfus has a box that contains cards of the same shape and size.there are 5 yellow cards, 4red cards, and 1 purple card.he draws a card at random replaced it, and draws a second card .what is the probability that both cards will be red?

Answer 1

Answer:

$P(Red\ and\ Red) = \frac{4}{25}$

Step-by-step explanation:

Given

$Yellow = 5$

$Red = 4$

$Purple = 1$

$Total = 10$

Required

Determine the probability of selecting red, twice

Since it is a probability with replacement, the probability can be represented as:

$P(Red\ and\ Red) = P(Red) * P(Red)$

And this is calculated as follows:

$P(Red\ and\ Red) = \frac{n(Red)}{Total} * \frac{n(Red)}{Total}$

$P(Red\ and\ Red) = \frac{4}{10} * \frac{4}{10}$

$P(Red\ and\ Red) = \frac{2}{5} * \frac{2}{5}$

$P(Red\ and\ Red) = \frac{4}{25}$