Need Help on Probability Probs.

[ajk003]

:confused: I'm having trouble with some problems:

1) Suppose that in a family, the probability of a child having black hair is .45, the probability of a child having blonde hair is .3 the probability of having red hair is .1, and the probability of a child having green hair is .15. If this family has two children, what is the probability that both children will have the same hair color?

I'm not sure how to approach this problem..
The different probabilities of each color is confusing me. I know that if all four of them had a same probability of .25, I would do (.25)(.25)=.0625..

2) If you roll a fair, six-sided die 5 times, then what is the probability that you will NOT get the same result on every roll?

For this problem I did (1/6)(2/6)(3/6)(4/6)(5/6)= 0.0154... But not sure if it is correct. Please Help!!

[JohnM]

1) Writing this out, it's:

P(black and black) or P(blonde and blonde) or P(red and red) or P(green and green)

= (.45 * .45) + (.3 * .3) + (.1 * .1) + (.15 * .15)

2) When you roll a die 5 times, there are a total of 6^5 = 7776 possible outcomes. There are 6 ways that you could get the same outcome on all 5 rolls (11111,22222,33333,44444,55555,66666), so it's:

= (7776 - 6) / 7776

= 7770 / 7776

[ajk003]

Thanks so much! but for the second problem I need to find the probability of 5 different outcomes instead of 5 same outcomes. So then would my approach be correct?

[JohnM]

OK, if it's 5 different outcomes on each roll, then it's:

= (6 * 5 * 4 * 3 * 2) / 6^5

= 720 / 7776

[ajk003]

for the first problem, if the probability of having each color of hair is all .25 (same for all colors), then would I do (.25)(.25) to find out the probability of two children having the same hair color, or would I add them? When would I add and when would I multiply?

[JohnM]

You would follow the same method I posted, but it would be:

= (.25 * .25) + (.25 * .25) + (.25 * .25) + (.25 * .25)

Generally, when it's "and" you multiply, when it's "or" you add.

[ajk003]

Thank you so much! :)
That really helped a lot!

[lepinheiro]

A salesperson makes four calls a day. The probability that she makes a sale on the first call is .5:

- If she fails on the first call, she gets discouraged and the probability that she makes a sale on any other call drops to 1/4.
- if she succeeds on the first call, then the probability that she succeeds on any other call is .5

What is the probability that the salesperson makes at least one sale on a given day?

Can you also tell me how do you know when to multiply or add.