Question

Event A: Spinning violet or yellow on the spinner.

Event B: Rolling an even number on a number cube.


What is P(A and B)?

Answer 1

P(A)

• 2/4
• 1/2
• 0.5

P(B)

3 even nos are 2,4,6

• 3/6
• 1/2
• 0.5

P(A
`\cap`)

• 0.5²
• 0.25 or 1/4

Answer 2

`\sf P(A \cap B)=(1)/(4)`

Explanation:

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

Event A - spinning violet or yellow

Assuming that the spinner has 4 different colors (red, orange, violet and yellow) - see attachment.

`\implies \sf P(A) = (2)/(4)=(1)/(2)`

Event B - rolling an even number

Assuming the number cube has 6 sides numbered 1, 2, 3, 4, 5 and 6. Therefore, the even numbers are 2, 4 and 6.

`\implies \sf P(B)=(3)/(6)=(1)/(2)`

Events A and B are independent events as the outcome of one event does not affect the outcome of the other event.

For independent events A and B:

`\implies \sf P(A \cap B)=P(A)P(B)`

To find P(A and B), substitute the found values of P(A) and P(B):

`\implies \sf P(A \cap B)=(1)/(2) * (1)/(2)=(1)/(4)`