Question

A cereal company puts a special prize into 1 out of 20 boxes of its children's cereals. Your buy 10 boxes, hoping to find a card. A success is opening a box and finding one of these prizes.

(a) What is "p", the probability of success? (express as a decimal, 2 decimal places)


(b) What is the probability of failure? (express as a decimal, 2 decimal places)


(c) What is the probability you will not find any of the cards in the 10 boxes you buy? P(X = 0) = (express as a decimal, use 2 decimal places)

(d) Which expression shows the correct use of the binomial formula for P(X = 2) in Excel? (can be found in the course notes)

=binom.dist(2, 0.02, 15, TRUE) =binom.dist(2, 10, 0.05, FALSE)     =binom.dist(2, 0.20, 10, FALSE) =binom.dist(2, 10, 0.05, TRUE) =binom.dist(10, 2, 0.05, FALSE)

Answer 1

(a) If the company puts a special prize into 1 out of 20 boxes, the probability of opening a box and finding one of these prizes will be 1 in 20 i.e. 1/20.

Therefore, if success is opening a box and finding one of these prizes.

Then, Probability of Success (p) = 1/20 = 0.05

(b) Probability of Failure + Probability of Success = 1

Probability of Failure + p = 1

Probability of Failure = 1 - p = 1 - 0.05 = 0.95

Probability of Failure = 0.95

(c) Probability that you will not find any card in the 10 boxes you buy will be P(X=0).

Now, If p is the probability of success. Then the probability of success of X trials out of a total of N trials will be .

There are 10 boxes bought. Therefore N = 10

If there is no card in any of the box then X = 0.

And p = 0.05.

Therefore, P(X=0) =

P(X=0) = = 0.599 = 0.60.

(d) BINOM.DIST(Number_s,Trials,Probability_s,Cumulative) is the formula for binomial in excel.

Where, Number_s is number of successful trials; Trials is the number of trials; Probability_s is the probability of success and cumulative is a logical value true for cumulative distribution function and false for probability mass function.

For P(X=2) means probability of finding cards in 2 boxes out of 10 boxes.

Number_s = 2

Trials = 10

Probability_s = 0.05

Cumulative = False

Therefore, Binom.dist(2,10,0.05,false) is the Excel Formula.

Do comment for any doubts.