The credit department of Lion's Department Store in Anaheim, California, reported that 30% of their sales are cash, 30% are paid with a credit card, and 40% with a debit card. Twenty percent of the cash purchases, 90% of the credit card purchases, and 60% of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability that she paid cash?

Hence the probability that she paid cash is  0.105

Step-by-step explanation:  

P(cash) = 0.3  

P(credit card ) = 0.3  

P(debit card ) = 0.4  

P ( more than $50 | cash ) = 0.2  

P (more than $50 | credit card ) =0.9  

P (more than $ 50 |debit card ) = 0.6  

P ( more than $50) = P ( more than $50 | cash )* P (cash) + P (more than $50 credit card ) * P(credit card ) + P (more than $ 50 |debit card )* P(debit card )  

= 0.2 * 0.3 + 0.9 * 0.3 + 0.6* 0.4  

= 0.57  

P ( more than $50) = P ( more than $50 | cash )* P (cash) / P ( more than $50)  

= 0.2* 0.3 / 0.57  

= 0.105

(a) Surface energy is greater than grain boundary energy due to the fact that the bonds of the atoms on the surface are lower than those of the atoms at the grain boundary. The energy is also directly proportional to the number of bonds created.

(b) The energy of a high-angle grain boundary is higher than that of a small-angle grain boundary because the high-angle grain boundary has a higher misalignment and smaller number of bonds than a small-angle grain boundary.

Explanation:

(a) Surface energy is greater than grain boundary energy due to the fact that the bonds of the atoms on the surface are lower than those of the atoms at the grain boundary. The energy is also directly proportional to the number of bonds created.

(b) The energy of a high-angle grain boundary is higher than that of a small-angle grain boundary because the high-angle grain boundary has a higher misalignment and smaller number of bonds than a small-angle grain boundary.