Probability... (1 Viewer)

[azureus88]

Five families have 3 children each. Find the probability that at least one of these families has 3 boys.

The answer's 0.487 but how do you get it?

 

[Trebla]

Draw a probability tree if it helps to visualise it.

P(at least one having 3 boys) = 1 - P(all not having 3 boys)

Assume the probability of having a girl is equal to the probability of having a boy.
The probability of one family NOT having 3 boys is: 1 - (0.5)³ = 0.875
There are 5 families so the probability all of them do not have 3 boys is at the same time is:
P(all not having 3 boys) = (0.875)⁵

Hence:
P(at least one having 3 boys) = 1 - (0.875)⁵ ~ 0.487

 

[azureus88]

I got another question if u dont mind... it rains on average 18 out of 30 days. 5 days are chosen at random. Find the probability that its fine on the first 2 days and rains on the remainder days. y isnt it [(12/30)^2][(18/30)^3]?

 

[lyounamu]

I got another question if u dont mind... it rains on average 18 out of 30 days. 5 days are chosen at random. Find the probability that its fine on the first 2 days and rains on the remainder days. y isnt it [(12/30)^2][(18/30)^3]?

Nope.

You have to use binomial theorem for this.

It's like

5c3 (12/30)^2 (18/20)^3

 

[lolokay]

I got another question if u dont mind... it rains on average 18 out of 30 days. 5 days are chosen at random. Find the probability that its fine on the first 2 days and rains on the remainder days. y isnt it [(12/30)^2][(18/30)^3]?

your answer sounds correct to me. they give you the order of days so you don't need to bother with the combinations (5C3)

 

[lyounamu]

your answer sounds correct to me. they give you the order of days so you don't need to bother with the combinations (5C3)

Gah, didn't read the "first" part of the sentence.

And if his answer was not right, I thought mine would have been.

 

[azureus88]

hm...the answers actually 0.0124, unless its a typo...