Get the solution to "a) To find the probability of winning at..."

Nann

Answered question

2021-09-26

a) To find the probability of winning at least one prize if you purchase 10 tickets.
b) To find the probability of winning at least one prize if you purchase 15 tickets.

Answer & Explanation

Alannej

Skilled2021-09-27Added 104 answers

a) Given:
For a particular lottery, 1/10 of the 50 million tickets will win a prize.
Concept used:
Binomial probability:
$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) \cdot p^{x} \cdot (1 - p)^{n - x}$
Complement rule:
$P (A^{'}) = 1 - P (A)$
Calculation:
Let X is the random variable that denotes the number of wins.
Clearly, X has the binomial distribution with
$n = 10 and p = \frac{1}{10} = 0.1$
Now the probabillity of winning at least one prize if you purchase 10 tickets is,
$P (X \geq 1) = 1 - P (X = 0)$
$= 1 - (\begin{matrix} 10 \\ 0 \end{matrix}) \cdot (0.1)^{0} \cdot (1 - 0.1)^{10 - 0}$
$= 1 - {(0.9)}^{10}$
$= 1 - 0.3486784401$
$= 0.6513215599$
$\approx 0.65$
b) Given:
For a particular lottery, 1/10 of the 50 million tickets will win a prize.
Concept used:
Binomial probability:
$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) \cdot p^{x} \cdot (1 - p)^{n - x}$
Complement rule:
$P (A^{'}) = 1 - P (A)$
Calculation:
Let X is the random variable that denotes the number of wins.
Clearly, X has the binomial distribution with
$n = 15 and p = \frac{1}{10} = 0.1$
Now the probabillity of winning at least one prize if you purchase 15 tickets is,
$P (X \geq 1) = 1 - P (X = 0)$
$= 1 - (\begin{matrix} 15 \\ 0 \end{matrix}) \cdot (0.1)^{0} \cdot (1 - 0.1)^{15 - 0}$
$= 1 - {(0.9)}^{15}$
$= 1 - 0.2058911321$
$= 0.7941088679$
$= 0.79$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Didn't find what you were looking for?