Question

Question:

(a) To determine the probability that a player who has buys a mega million ticket and megaplier wins \( 5000000.

(b)To determine the probability that a player who has buys a mega million ticket and megaplier wins \) 30000.

(c)To determine the probability that a player who has buys a mega million ticket and megaplier wins \( 20

(d) To determine the probability that a player who has buys a mega million ticket and megaplier wins \) 8.

Short answer

Answer

(a) The probability that a player who has buys a mega million ticket and megaplier wins $ 5000000 is$0.000015$.

(b)The probability that a player who has buys a mega million ticket and megaplier wins $ 30000 is$0.0006954$.

(c)The probability that a player who has buys a mega million ticket and megaplier wins $ 20 is$0.00001456$.

(d) The probability that a player who has buys a mega million ticket and megaplier wins $ 8 is$0.000006577$.

Step-by-step solution

 Given  

(a) A player who has buys a mega million ticket and megaplier wins.

(b) A player who has buys a mega million ticket and megaplier wins.

(c) A player who has buys a mega million ticket and megaplier wins.

(d) A player who has buys a mega million ticket and megaplier wins.

The Concept of probability

If $\mathit{S}$represents the sample space and$\mathit{E}$represents the event. Then the probability of occurrence of favourable event is given by the formula as below:

.$\mathit{P}\mathbf{\left(}\mathit{E}\mathbf{\right)}\mathbf{=}\frac{\mathbf{n}\mathbf{\left(}\mathbf{E}\mathbf{\right)}}{\mathbf{n}\mathbf{\left(}\mathbf{S}\mathbf{\right)}}$

The probability of winning a lottery (b)

The probability that a player who has buys a mega million ticket and megaplier wins $ 30000.

The only Way to do this is to match exactly three of the first five number drawn and the sixth number drawn with megaplier3X.

$$\begin{gathered} C(40,4)=\frac{40!}{4!36!} \\ C(15,3)=\frac{15!}{3!12!} \end{gathered}$$

Use product rule found 56

$p=0.0006954$

The probability of winning a lottery (c)

The probability that a player who has buys a mega million ticket and megaplier wins $ 20.

He only Way to do this is to match exactly three of the first five number drawn and but not the sixth number or exactly two of the first five number and sixth number with megaplier 2X, to match exactly the first five number drawn and the sixth number drawn with megaplier 5X.

$$\begin{gathered} C(42,4)=\frac{42!}{4!38!} \\ C(5,2)=\frac{5!}{2!3!} \end{gathered}$$

Use product rule found 106

.$\text{p}=0.00001456$

The probability of winning a lottery (d)

The probability that a player who has buys a mega million ticket and megaplier wins $ 8.

The only Way to do this is to match exactly three of the first five number drawn and the sixth number drawn with megaplier2X, or match the sixth number but none of the first five number with megaplier

$$\begin{gathered} C(43,5)=\frac{42!}{5!38!} \\ C(5,1)=\frac{5!}{1!4!} \end{gathered}$$

Use product rule found 97

$\text{p}=0.000006577$