Zara runs a home business based on art and craft items. She sells her

puntgewelb5

puntgewelb5

Answered question

2021-12-06

Zara runs a home business based on art and craft items. She sells her products either through taking orders online from her website or art exhibitions. Based on her previous data, 40% of the orders are received from art exhibitions. Suppose 18 orders were booked independently, what is the probability that
a) Between eight and ten orders were booked through website?
b) What is the probability that the 3-rd order placed is the first order booked from website?
c) What is the probability that the 8-th order placed is the fourth order booked from website?

Answer & Explanation

David Tyson

David Tyson

Beginner2021-12-07Added 19 answers

Step 1
Consider X be a random variable which follows binomial distribution indicates the number of orders booked. The number of trials, n is 18 and the probability of success, p is 0.40.
The binomial distribution formula is used here,
P(X=x)=nCxpx(1p)nx
Step 2
a) The probability that between eight and ten orders were booked through website is,
P(8X10)=P(X=8)+P(X=9)+P(X=10)
=(18C8(0.4)8(10.4)188+18C8(0.4)8(10.4)188+18C8(0.4)8(10.4)188)
=0.1734+0.1284+0.0771
=0.3789
Step 3
b) The probability that the 3rd order placed is the first order booked from website is P(X=3) where X is the geometric random variable with parameter, p=0.4.
P(X=x)=(1p)x1p
P(X=3)=(10.4)31(0.4)
=0.144
Step 4
c) The probability that the 8th order placed is the 4th order booked from website is,
P(8th order is 4th website order)=P(first 7 orders is a combination of 3 internet orders and 4 other orders)×P(8th order from website)
=(10.4)4(0.4)3(0.4)
=0.0033

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