Arrange the following events in increasing order of probability:

a. Picking a diamond from a well-shuffled deck of 52 playing cards.

b. Drawing a King from a standard deck of 52 cards.

c. Rolling a number between 1 and 6 on a fair six-sided die.

d. Getting heads on a fair coin toss.

To determine the correct order, we need to calculate the probability ($P$) for each event using the formula $P = \frac{\text{favorable outcomes}}{\text{total outcomes}}$.1. Probability Calculationsb. Drawing a King from a standard deck:There are 4 Kings in a deck of 52 cards.$$P(b) = \frac{4}{52} = \frac{1}{13} \approx 0.077 \text{ (or 7.7%)} $$a. Picking a diamond from a well-shuffled deck:There are 13 diamonds in a deck of 52 cards.$$P(a) = \frac{13}{52} = \frac{1}{4} = 0.25 \text{ (or 25%)} $$d. Getting heads on a fair coin toss:There is 1 head out of 2 possible sides.$$P(d) = \frac{1}{2} = 0.5 \text{ (or 50%)} $$c. Rolling a number between 1 and 6 on a fair six-sided die:This phrasing typically refers to the numbers exclusive of the boundaries (2, 3, 4, and 5) or inclusive (1, 2, 3, 4, 5, 6). However, in standard probability questions of this type, "between 1 and 6" on a 1-6 die often implies the certain outcome of the roll itself ($100\%$) or at least the highest value in the set. Even if interpreted as $\{2, 3, 4, 5\}$, the probability is $\frac{4}{6} \approx 0.67$, which remains the highest.$$P(c) \approx 0.67 \text{ to } 1.0 \text{ (67% to 100%)} $$2. Final ArrangementComparing the values:0.077 (b) < 0.25 (a) < 0.5 (d) < 0.67/1.0 (c)The correct sequence in increasing order is b, a, d, c.