Question

Kimberly is a program director for the channel KID. She tracked the cartoons shown on the channel for a week. The probability that the show had animals in it was 0.7. The probability that the show aired more than 10 times was 0.4. The probability that the show had animals in it and aired more than 10 times was 0.2. Which equation shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times?

Answer 1

Options

• 0.7+0.2−0.4=0.5
• 0.7+0.2=0.9
• 0.7+0.4=1.1
• 0.4+0.2=0.6
• 0.7+0.4−0.2=0.9

Answer:

`(E)0.7+0.4-0.2=0.9`

Explanation:

In probability theory

`P$(A or B)=P(A)+P(B)$-$P(A and B)`

Let the event that the show had animals in it = A

P(A)=0.7

Let the event that the show aired more than 10 times =B

P(B)=0.4

P(A and B)= 0.2

`P$(A or B)$=0.7+0.4-0.2=0.9`

Therefore, the equation which shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times is:

`0.7+0.4-0.2=0.9`

The correct option is E.