The probability that the Sun and Moon appear to be the same size in the sky is quite low. This phenomenon, known as a total solar eclipse, occurs when the apparent size of the Moon matches the apparent size of the Sun, resulting in the Moon fully blocking the Sun's disk.
The reason the probability is low is because of the significant difference in the sizes of the Sun and Moon and their respective distances from Earth. The Sun has a diameter of about 1.4 million kilometers (870,000 miles), while the Moon has a diameter of about 3,474 kilometers (2,159 miles). The Sun is also approximately 400 times larger in diameter than the Moon.
Additionally, the Moon's orbit around the Earth is elliptical, causing its distance from Earth to vary. When the Moon is closer to Earth (at perigee), it appears slightly larger than when it is farther away (at apogee). The Sun, on the other hand, remains relatively constant in its distance from Earth.
The alignment required for a total solar eclipse is when the Moon is at the right distance and position to fully block the Sun's disk as seen from a specific location on Earth. This alignment is relatively rare, and the path of totality, where a total solar eclipse can be observed, is usually narrow and covers a small percentage of the Earth's surface.
On average, a total solar eclipse occurs somewhere on Earth roughly every 18 months, but the probability of observing it at a specific location is much lower. The occurrence and visibility of a total solar eclipse depend on various factors, including the positions and movements of the Sun, Moon, and Earth.
It's worth noting that there are other types of solar eclipses, such as partial and annular eclipses, where the apparent sizes of the Sun and Moon do not match, resulting in a partial or ring-shaped eclipse, respectively. These types of eclipses are more common than total solar eclipses.