Question

Event A: Spinning violet or yellow on the spinner.

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

Answer:

$\sf P(A \cap B)=\dfrac{1}{4}$

Step-by-step explanation:

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Event A - spinning violet or yellow

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

$\implies \sf P(A) = \dfrac{2}{4}=\dfrac{1}{2}$

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.

$\implies \sf P(B)=\dfrac{3}{6}=\dfrac{1}{2}$

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):

$\implies \sf P(A \cap B)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}$