What Is the Probability That a Mango Weighing Under 492g Is Red?

[denian]

im during direct traslation from my language to english. hope you can understand the question.


Orchard A produces red mangoes. the mass of the red mango is distributed normally with mean 500g and standard deviation 10g
Orchard B produces yellow mangoes. the mass of the yellow mango is distributed normally with mean 490g and standard deviation 6g

(i) show that probability that the mass of a red mango chosen at random is less than 472g = 0.212

# i have proven this part.

(ii) a lorry collects mangoes from both orchard. amount of red mangoes collected is two times than the amount of yellow mangoes collected. if one mangoes is picked at random from the mangoes collected and its mass is less than 492g, find the probability that the mango is red mango.

# please help me with this one. thx.

 

[denian]

i don't have the answer for this question actually. and i just hope to know the way to solve it. thx.

 

[Galileo]

Use the formula for conditional probability:

Given the mass of the mango is less than 492g, what is the probability it will be red?
In general the probability of an event A conditioned on C is:
$$P(A|C)=\frac{P(A \cup C)}{P(C)}$$

In this problem, A would be the event of picking a red mango and
C would be the event of picking a mango with a mass less than 492g.

 

[denian]

sorry. I am still blur.
how to find $$P(A \cup C)$$?

the marks given for this question is 5. so, i think the working is long.

 

[Galileo]

I`m sorry, that should've been:

$$P(A|C)=\frac{P(A \cap C)}{P(C)}$$

$P(A \cap C)$ is the probability of getting a red mango which weighs less than 492g.
You could use:
$$P(C|A)=\frac{p(A \cap C)}{P(A)}$$
and combine with the above to give:
$$P(A|C)=\frac{P(C|A)P(A)}{P(C)}$$

Hope that helps

 

[denian]

thanks. i have try first.

 

[denian]

probability question. pls help to check

im sorry. i still not able to solve it. can u show me ur whole working.. sorry..