Probabilities are used to determine the chances of an event.
The probability of selecting a yellow and not a red peg is: 0.1625
The probabilities are given as:
[tex]\mathbf{P(red) = 0.35}[/tex]
[tex]\mathbf{P(green) = 0.4}[/tex]
The probability of selecting yellow is calculated as follows:
[tex]\mathbf{P(green) + P(red) + P(yellow) = 1}[/tex]
Substitute known values
[tex]\mathbf{0.4+ 0.35 + P(yellow) = 1}[/tex]
[tex]\mathbf{0.75 + P(yellow) = 1}[/tex]
Subtract 0.75 from both sides
[tex]\mathbf{P(yellow) = 0.25}[/tex]
The probability of selecting a yellow and not a red peg is:
[tex]\mathbf{P(Yellow\ n\ Not\ Red) = P(Yellow) \times P(Not\ Red)}[/tex]
Using the complement rule, we have:
[tex]\mathbf{P(Yellow\ n\ Not\ Red) = P(Yellow) \times (1 - P(Red))}[/tex]
Substitute known values
[tex]\mathbf{P(Yellow\ n\ Not\ Red) =0.25 \times (1 - 0.35)}[/tex]
[tex]\mathbf{P(Yellow\ n\ Not\ Red) =0.25 \times 0.65}[/tex]
[tex]\mathbf{P(Yellow\ n\ Not\ Red) =0.1625}[/tex]
Hence, the probability of selecting a yellow and not a red peg is: 0.1625
Read more about probabilities at:
https://brainly.com/question/11234923
