Which is most likely, two coins both landing heads up or a picture card being chosen at random from a full deck?

Question

Each of three bags b1, b2, b3 contains only red and blue balls in the quantities:

Bag b1
red = 2 balls
blue = x2 – 6x + 13 balls

Bag b2
red = 3 balls
blue = x2 – 6x + 12 balls

Bag b3
red = 4 balls
blue = x2 – 6x + 11 balls

A ball is drawn at random from a randomly chosen bag. What is the maximum probability the drawn ball is red?

Answer 1

All the possible coin outcomes = (HH, TH, HT, TT)
Therefore the probability that 2 coins will land on head = (1/4) = 0.25

There are 52 cards in total in a deck, 13 cards in each type & each type has 4 picture cards. This means there are 4×4 =16 cards out of 52 that are picture cards. This makes the probability of picking a picture card randomly from a complete deck = (16/52) = 0.3077

Since 0.3077 > 0.25 it is more likely for a person to pick a picture card out of a deck than landing 2 coins with heads up.