Question

Bartholemew will draw with replacement 160 tickets at random from a box with five tickets [0, 0, 0, 1, 2]. Estimate the chance that the ticket with the 1 on it turns up on exactly 32 draws. Show your work. Please round your answer to the nearest whole percent. (Do not write the % sign, just the whole number.)

Answer 1

0.0786

Explanation:

It is given that Bartholemew had drawn the replacement of 160 tickets.

There are five tickets = [0, 0, 0, 1, 2]

Now we need to find the estimate of the ticket that has 1 on it and it turns up on the 32 draws exactly.

Since the probability of the drawing 1 out of 5 tickets is given by,
`$(1)/(5) = 0.2$`

So the binomial with the parameter of n = 160 and p = 0.2, we get

P (it turns up on exactly 32 draws) = P(X = 32)

Therefore,

`$C(160, 32)* (0.2)^(32)* (0.8)^(160-32)$`

= 0.0786