the digits 0 to 9
P(obtaining a prime number OR obtaining an odd number)
P(obtaining a prime number OR obtaining a number divisible by 4)
P(obtainig a number divisible by 4 or obtaining an odd number)
I will do the first one. The possible results are 1,2,3,5,7,9 . Any one of those is a prime or odd number
Pr= 6/10
this odd number
To find the probabilities of the given events, we need to determine the total number of outcomes and the number of favorable outcomes for each event.
First, let's consider the event of obtaining a prime number or obtaining an odd number.
1. P(obtaining a prime number OR obtaining an odd number):
- Count the favorable outcomes: There are four prime numbers (2, 3, 5, 7) and five odd numbers (1, 3, 5, 7, 9) in the given digits.
- Total number of outcomes: There are ten digits from 0 to 9.
- So, P(obtaining a prime number OR obtaining an odd number) = (4 + 5) / 10 = 9/10.
Next, let's consider the event of obtaining a prime number or obtaining a number divisible by 4.
2. P(obtaining a prime number OR obtaining a number divisible by 4):
- Count the favorable outcomes: Apart from the previous prime numbers (2, 3, 5, 7), there are two numbers divisible by 4 (4, 8) in the given digits.
- Total number of outcomes: There are ten digits from 0 to 9.
- So, P(obtaining a prime number OR obtaining a number divisible by 4) = (4 + 2) / 10 = 6/10 = 3/5.
Lastly, let's consider the event of obtaining a number divisible by 4 or obtaining an odd number.
3. P(obtaining a number divisible by 4 OR obtaining an odd number):
- Count the favorable outcomes: There are two numbers divisible by 4 (4, 8) and five odd numbers (1, 3, 5, 7, 9) in the given digits.
- Total number of outcomes: There are ten digits from 0 to 9.
- So, P(obtaining a number divisible by 4 OR obtaining an odd number) = (2 + 5) / 10 = 7/10.
Therefore, the probabilities are:
1. P(obtaining a prime number OR obtaining an odd number) = 9/10.
2. P(obtaining a prime number OR obtaining a number divisible by 4) = 3/5.
3. P(obtaining a number divisible by 4 OR obtaining an odd number) = 7/10.