Question

A large fastfood restaurant is having a promotional game where game pieces can be found on various products customers can win food or cash prizes according to the company the probability of winning a prize larger small with any eligible purchases is 0.185 consider your next 29 purchases that produce a game piece calculate the following

Answer 1

The formula for binomial probability is expressed as

P(x) = nCx * p^x * q^(n - x)

where

n = number of trials

x = number of successes

p = probability of success

q = probability of failure

From the information given,

n = 29

p = 0.185

q = 1 - p = 1 - 0.185 = 0.815

a) For the probability that you win 6 prices, x = 6

P(x = 6) = 29C6 * 0.185^6 * 0.815^(29 - 6)

P(x = 6) = 0.1723

b) For the probability that you win more than 8 prices, x = 8. From the binomial probability distribution calculator,

`P(x>8)\text{ = 0.0729}`

c) we would find the probability that you win more than 4 prizes and subtract it from the probability that you win 7 or lesser pizes. x = 4 and x = 7

From the binomial probability distribution calculator,

`\begin{gathered} P(x>4)\text{ = 0}.6438 \\ P(x\text{ }\leq7)\text{ = 0.8468} \\ P(4\text{ }\leq\text{ x }\leq7)\text{ = 0.8468 - 0.6438 = 0}.203 \end{gathered}`

d) For the probability that you win 3 prizes or fewer, x = 3. From the binomial probability distribution calculator,

`P(x\leq3)\text{ = 0}.1890`