Question

Give the numerical value of the parameter p in the following binomial distribution scenario.

The probability of winning an arcade game is 0.632 and the probability of losing is 0.368. If you play the arcade game 10 times, we want to know the probability of winning no more than 8 times.

Consider winning as a success in the binomial distribution. Do not include p= in your answer.

Answer 1

Answer:0.9306

Explanation:

Given

Probability of winning
`p=0.632`

Probability of losing
`q=0.368`

Such that
`p+q=1`

Applying binomioal distribution for n=10 trials

Probability of winning no more than 8 time=P

`P(r\leq 8)+P(r>8)=1`

`P(r\leq 8)=1-P(r>8)`

`P(r\leq 8)=1-^(10)C_9(p)^9(q)-^(10)C_(10)(p)^(10)(q)^0`

`P(r\leq 8)=1-^(10)C_9(0.632)^9(0.368)-^(10)C_(10)(0.632)^(10)(0.368)^0`

`P=P(r\leq 8)=0.9306`