Problem: Find the probability of drawing a card numbered from 7 to 51 that is divisible by 2 or 3.

Solution:

To find the probability, we need to determine the total number of favorable outcomes and the total number of possible outcomes.

Total Number of Possible Outcomes:
The total number of cards in the deck is 51-7+1 = 45. Therefore, there are 45 possible outcomes.

Total Number of Favorable Outcomes:
We need to determine the number of cards that are divisible by 2 or 3 between 7 and 51.

Divisible by 2:
The numbers divisible by 2 between 7 and 51 are:
8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50.

There are 22 cards divisible by 2.

Divisible by 3:
The numbers divisible by 3 between 7 and 51 are:
9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51.

There are 15 cards divisible by 3.

Numbers Divisible by 2 and 3:
To avoid double counting, we need to find the numbers that are divisible by both 2 and 3.

The numbers divisible by both 2 and 3 (i.e., divisible by 6) between 7 and 51 are:
12, 18, 24, 30, 36, 42, 48.

There are 7 cards divisible by both 2 and 3.

Calculating the Probability:
To find the probability, we divide the number of favorable outcomes by the number of possible outcomes.

Total Number of Favorable Outcomes = Number of cards divisible by 2 + Number of cards divisible by 3 - Number of cards divisible by both 2 and 3
= 22 + 15 - 7
= 30

Probability = Total Number of Favorable Outcomes / Total Number of Possible Outcomes
= 30 / 45
= 2/3

Therefore, the probability of drawing a card numbered from 7 to 51 that is divisible by 2 or 3 is 2/3.

30/45=2/3