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 lion, both with and without replacement.
two cards are to be selected without replacement. determine the probability that both cards selected have a lion.
(type an integer or a simplified fraction.)
two cards are to be selected with replacement. determine the probability that both cards selected have a lion.
(type an integer or a simplified fraction.)

Explanation:

Answer:

The discipline is Mathematics, and the sub - field is Statistics. The probability that both cards selected without replacement have a 1:
The total number of cards is \(n = 20\). The number of cards with a 1 is \(m=4\).
The probability that the first card has a 1 is \(\frac{4}{20}\). After the first card is drawn (without replacement), there are 19 cards left and 3 cards with a 1 left. So the probability that the second card has a 1 given that the first card had a 1 is \(\frac{3}{19}\).
The probability that both cards have a 1 is \(\frac{4}{20}\times\frac{3}{19}=\frac{12}{380}=\frac{3}{95}\)