Question

a board game uses the deck of 20 cards shown to the right. two cards are selected at random from this deck. calculate the probability that both cards selected have a frog, both with and without replacement.

two cards are to be selected with replacement. determine the probability that both cards selected have a frog.

(type an integer or a simplified fraction.)

Explanation:

Count the total cards and target cards

Using the Theoretical Probability knowledge point

• Total number of cards in the deck: \(N = 20\)
• Number of cards with a frog (green animals in the third row, numbered 1 to 5): \(n = 5\)

Calculate the probability of selecting a frog on a single draw

Using the Fraction Simplification knowledge point

$$ P(\text{Frog}) = \frac{5}{20} = \frac{1}{4} $$

Calculate the probability with replacement

Using the Independent Events knowledge point

$$ P(\text{Both Frogs}) = P(\text{Frog}) \times P(\text{Frog}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} $$

Answer:

Two cards are to be selected with replacement. Determine the probability that both cards selected have a frog.

<blank>\(\frac{1}{16}\)</blank> (Type an integer or a simplified fraction.)