Independent event and mutually exclusive event

[kingwinner]

This is my second class in intro to probability at a university level.

1) There are 5 people in a room with 3 boys and 2 girls. If I randomly pick 1 person from the box, P(boy)=3/5. If I randomly pick 2 people, P(pick 2 girls) = 2/5 x 1/4 = 1/10.

a) Now what is P(pick 1 girl and 1 boy) equal to if the order doesn't matter?

b) What is P(pick 1 girl and 1 boy) equal to if the order does matter?
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1a) My guess is that P(pick 1 girl and 1 boy) = 2/5 x 3/4 = 6/20 = 3/10 if the order doesn't matter. Is this right?

1b) No idea...

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2) What is the difference between an "independent event" and a "mutually exclusive event"? I can't visualize the difference...


Can someone help me please?

 

[D H]

1a. You made the order matter. Double check your answer: What are the only possible outcomes if you pick 2 people, and order doesn't matter? (Hint: three mutually exclusive events.) The probabilities for these exclusive events had better add to one.

1b. Once you get the answer correct for 1a. you should get this easily.

2. You shouldn't rely on us so much. A quick google search revealed multiple sites that give a very good explanation. A little research on your own part would help you a lot more than us spoonfeeding you the answers.

 

[kingwinner]

1a) (2/5 x 3/4) x 2 = 12/20 = 3/5 ?

1b) 2/5 x 3/4 = 3/10 ?

 

[D H]

You have the correct answers, but by guessing. If order does matter, there are four possible outcomes: <B,B>, <B,G>, <G,B>, and <G,G>. You calculated the probability of the <G,B> outcome correctly in 1b) as 2/5 x 3/4. The probability of the <B,G> outcome is 3/5 x 2/4. The order-insensitive outcome (G,B) is the union of the two mutually exclusive <B,G> and <G,B> outcomes. Adding the probabilities (valid since the events are mutually exclusive), P((G,B)) = P(<G,B>)+P(<B,G>) = 2/5 x 3/4 + 3/5 x 2/4 = 3/5.