Question

consider the tennis balls shown in the accompanying figure. assume that one tennis ball is randomly selected.
a) determine the probability that the ball selected shows an even number.
b) determine the probability that the ball selected shows an even number, given that the ball is green.
a) the probability that the ball selected shows an even number is □
(type an integer or a simplified fraction.)

Explanation:

Step1: Count total number of balls

There are \(6\) balls in total.

Step2: Count number of balls with even numbers

The even - numbered balls are \(2\), \(4\). So there are \(2\) even - numbered balls.

Step3: Calculate probability for part (a)

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the number of all possible outcomes. For part (a), \(n(A) = 2\) (even - numbered balls) and \(n(S)=6\) (total balls). So \(P=\frac{2}{6}=\frac{1}{3}\).

Step4: For part (b)

Given that the ball is green. The green balls are \(1\) and \(6\). Among them, the even - numbered green ball is \(6\). So \(n(A) = 1\) (even - numbered green ball) and \(n(S)=2\) (green balls). The probability \(P=\frac{1}{2}\).

Answer:

a) \(\frac{1}{3}\)
b) \(\frac{1}{2}\)