Question

In a batch of 100 parts, 40 are red, 50 are L-shaped and 22 are both red and L-shaped. What is probability that a part picked from this batch at random is either red or L-shaped

Answer 1

The probability that a part picked from this batch at random is either red or L-shaped is 0.68

Step-by-step explanation:

Let us revise some rules of probability

The addition rules are:

• P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen  at the same time)
• P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they  have at least one outcome in common)

∵ A batch has 100 parts

∵ 40 are red

- Probability of an event is the [even occurs/total outcomes]

∴ P(red) = $\frac{40}{100}=0.4$

∵ 50 are L-shaped

∴ P(L-shaped) = $\frac{50}{100}=0.5$

∵ 22 are both red and L-shaped

∴ P(red and L-shaped) = $\frac{22}{100}=0.22$

This is non-mutually exclusive because there is a common between them, so we will use the 2nd rule

∵ P(red or L-shaped) = P(red) + P(L-shaped) - P(red and L-shaped)

∴ P(red or L-shaped) = 0.4 + 0.5 - 0.22

∴ P(red or L-shaped) = 0.68

The probability that a part picked from this batch at random is either red or L-shaped is 0.68

Learn more:

You can learn more about the probability in brainly.com/question/2254182

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