Question

A LEGO action figure is created for visitors that tour a factory. Each figure consists of a randomly chosen set of legs, body, head, and hair/hat. The following table shows the available options for each category.

If each option is equally likely within each category what is the probability that the LEGO figure does NOT have blue legs but has a red body.

1/6

1/9

1/10

1/3

Answer 1

Answer:

1/3

Step-by-step explanation:

P(red body AND not blue legs) = P(red body) × P(not blue legs)

P = (1/2) × (2/3)

P = 1/3

Answer 2

Answer:  $\dfrac{1}{3}$

Step-by-step explanation:

From he given table,

Types of legs ( blue , red , black) = 3

Number of legs other than blue = 3-1=2

Types of body (red and blue) = 2

Probability that LEGO figure does NOT have blue legs :-

$\text{P(not blue legs)}=\dfrac{\text{Legs other than blue}}{\text{Total types of legs}}\\\\=\dfrac{2}{3}$

Similarly, Probability that LEGO figure has a red body :-

$\text{P(red body)}=\dfrac{1}{2}$

Since both the events are independent , then

Then probability that the LEGO figure does NOT have blue legs but has a red body will be :-

$\text{P(not blue legs and red body)=P(not blue legs) x P(red body)}\\\\=\dfrac{2}{3}\times\dfrac{1}{2}=\dfrac{1}{3}$

Hence, the correct answer is $\dfrac{1}{3}$ .