Question

Given that the the sample space s is the ordered pairs of two whole numbers, the first from one to three and the second from one to four
It says let the event A=the sum is even and event B= the first number is prime
so A=?
and B=?

Answer 1

The sample space for given condition

s ={ (1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4)}

The event A : sum is even

A = { (1,1),(1,3),(2,2),(2,4),(3,1),(3,3)} = 6

B = { (2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4)} = 8

Answer 2

Let's first list all the possible outcomes in the sample space S, which consists of ordered pairs of two whole numbers as described:

S = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}

Now, we'll define the events A and B based on the given conditions:

Event A: The sum is even. To find the outcomes where the sum of the two numbers is even, we can consider the following pairs: (1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3). So, Event A consists of the pairs: {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3)}.

Event B: The first number is prime. The prime numbers between 1 and 3 are 2 and 3. So, Event B consists of the pairs: {(2, 1), (2, 2), (2, 3)}.

To summarize: Event A = {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3)} Event B = {(2, 1), (2, 2), (2, 3)}

Answer 3

To find the events A and B as described, let's first list all the ordered pairs in the sample space S:

Sample space S: {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}

Event A: The sum is even

For event A, we need to find all the ordered pairs whose sum is an even number.

Pairs with even sum:

• (1, 1) → Sum: 1 + 1 = 2 (even)

• (1, 3) → Sum: 1 + 3 = 4 (even)

• (2, 2) → Sum: 2 + 2 = 4 (even)

• (2, 4) → Sum: 2 + 4 = 6 (even)

• (3, 1) → Sum: 3 + 1 = 4 (even)

• (3, 3) → Sum: 3 + 3 = 6 (even)

Event A: {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3)}

Event B: The first number is prime

For event B, we need to find all the ordered pairs where the first number is a prime number.

Prime numbers from 1 to 3: 2, 3

Pairs with the first number as prime:

• (2, 1)

• (2, 2)

• (2, 3)

• (2, 4)

• (3, 1)

• (3, 2)

• (3, 3)

• (3, 4)

Event B: {(2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}

In summary:

• Event A (the sum is even): {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3)}

• Event B (the first number is prime): {(2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)