Question

Suppose the probability of winning a particular lottery is 1 in 18670901 30.888 I Juanita and Michelle each play the lottery on one particular evening, what is the probability thatboth will select the winning numbers if they make their selections independently of each other?The probability that both will select the winning numbers is approximately(Use scientific notation Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed)Help Me Solve ThisView an ExampleGet More HelpClear AllCheck Answer

Answer 1

The probability of wining is

$p(\text{ winning)=}\frac{1}{30888}$

since Juanita and Michele make their selections independently, the events are independent, so we can write:

$p(\text{Juanita wins AND Michelle wins)}=p(\text{Juanita wins)}\times p(\text{ Michelle wins)}$

which gives

$p(\text{Juanita wins AND Michelle wins)}=\frac{1}{30888}\times\frac{1}{30888}$

By making the products, this yields,

$p(\text{Juanita wins AND Michelle wins)}=1.048143\times10^{-9}$

and by rouding to the nearest hundread after the decimal point in this result, the probability is approximately:

$p(\text{Juanita wins AND Michelle wins)}=1.05\times10^{-9}$