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Problem #3: A bag contains six yellow jerseys numbered 1 to 6. The bag also contains four purple jerseys numbered 1
to 4. You randomly pick a jersey. What is the probability that the jersey is purple or has a number on it that is greater
than 2?

Respuesta :

frika

Answer:

0.8

Step-by-step explanation:

Consider events:

A = the jersey is purple

B = the jersey has a number on it that is greater than 2

This event are not independent, so

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Find the probabilities:

1. There are 4 purple jerseys and 10 jerseys in total, then

[tex]P(A)=\dfrac{4}{10}=0.4[/tex]

2. There are 4 yellow jerseys with numbers greater than 2 and 2 purple jerseys with numbers greater than 2, so there are 4 + 2 = 6 jerseys with numbers greater than 2.

[tex]P(B)=\dfrac{6}{10}=0.6[/tex]

3. [tex]A\cap B=[/tex] purple jersey has number greater than 2.

There are 2 purple jerseys with numbers greater than 2, so

[tex]P(A\cap B)=\dfrac{2}{10}=0.2[/tex]

If [tex]A\cup B=[/tex] the jersey is purple or has a number on it that is greater than 2, then

[tex]P(A\cup B)=0.4+0.6-0.2=0.8[/tex]

The probability that the jersey is purple or has a number on it that is greater than 2 is; 0.8

What is the Probability?

Let A be the event of a purple jersey being selected

Let B be the event of a jersey with number greater than 2

There are 4 purple jerseys and 10 jerseys in total. Thus;

P(A) = 4/10 = 0.4

Also, there are 4 yellow jerseys with numbers greater than 2 and 2 purple jerseys with numbers greater than 2. Thus;

Jerseys with numbers greater than 2 = 4 + 2 = 6 jerseys

Thus; P(B) = 6/10 = 0.6

Purple jersey has a number greater than 2 is;

P(A n B) = 2/10 = 0.2

Probability that the jersey is purple or has a number on it that is greater than 2 is; P(A u B) = 0.4 + 0.6 - 0.2 = 0.8

Read more about Conditional Probability at; https://brainly.com/question/23382435

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