The probability of giving birth to a boy is 1/2. what is the probability that a family with 5 children will have at least 2 boys?
a)about 81.3%
b)about 76.9%
c)about 62.5%
d)about 90.3%

0.78

Step-by-step explanation:

"The probability that a family with 5 children will have at least 2 boys" is equivalent to the complement 1 - P(family will have 1 or 0 boys).

We can use a calculator with statistical functions built in to calculate this probability.  The function needed is for binomial probability:  binom(n, p, x).

P(family will have 1 or 0 boys) = binomcdf(5, 0.5, {0, 1} ) produces two results:  one the probab. of having 0 boys and one the probab. of having 1 boy:  0.03125 and 0.1875.  We add these together, obtaining 0.21875.

Then we subtract this result from 1 to obtain The probability that a family with 5 children will have at least 2 boys:  1 - 0.21875 = 0.78125, which may be reasonably rounded off to 0.78.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9