Question

Find the probability of at least 2 girls in 7 births. Assume that male and female births are equally likely and that the births are independent events.
A) 0.063
B) 0.938
C) 0.773
D) 0.164

Answer 1

at least two means not none and not one
compute those, add them, then subtract from 1

Answer 2

none is \((\frac{1}{2})^7\) and exactly 1 is \(7\times (\frac{1}{2})^7\)

Answer 3

I still don't quite get it

Answer 4

ok
no girls means exactly 7 boys, i.e. a boy each time
just like saying you flip a coin 7 times and get all Heads

Answer 5

the probability of getting heads on any one coin is \(\frac{1}{2}\) and so the probability of getting 7 heads in a row is \((\frac{1}{2})^7\) and likewise the probability of getting 7 boys in a row is \((\frac{1}{2})^7\)

Answer 6

now the probability of getting exactly 1 girl is the same as the probability of getting exactly one tail when you toss a coin 7 times

Answer 7

that probability is \(7\times (\frac{1}{2})^7\) and the "7" in front is because the girl can be in any one of the 7 births, just like the probability that you get exactly 1 tail in 7 flips of a coin is \[7(\frac{1}{2})^7\]

Answer 8

add up those two numbers, subtract the result from 1, because "two or more" means not zero and not one

Answer 9

ok I am still confused on what to add up, can you just show how to get the answer?

Answer 10

\[1-\left(\frac{1}{2}\right)^7-7\times \left(\frac{1}{2}\right)^7\] and a calculator

Answer 11

ok so the 1/2 represents 1 of the girls birth out of 2 choices of a boy or girl.... but what is the 1- and the -7 represent?

Answer 12

i think i have lost you
suppose i asked instead, what is the probability that if you toss a coin 7 times you get all heads?
do you know how to compute that?

Answer 13

to compute that it would be (1/2)^7, my question is in the drawing