Company A supplies 40% of the computers sold and is late 5% of the time. Company B supplies 30% of the computers sold and is late 3% of the time. Company C supplies another 30% and is late 2.5% of the time. A computer arrives late - what is the probability that it came from Company A?
In Orange County, 51% of the adults are males. One adult is randomly selected for a survey involving credit card usage. It is later learned that the selected survey subject was smoking a cigar. Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the Substance Abuse and Mental Health Services Administration). Use this additional information to find the probability that the selected subject is a male.
A person uses his car 30% of the time, walks 30% of the time and rides the bus 40% of the time as he goes to work. He is late 10% of the time when he walks; he is late 3% of the time when he drives; and he is late 7% of the time he takes the bus.
In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
$1-0.45 = 0.55$
$\displaystyle{\frac{(0.55)(0.55)}{(0.45)((0.40)+(0.55)(0.55)} \doteq 0.627}$
On a game show, a contestant can select one of four boxes. The red box contains one $\$100$ bill and nine $\$1$ bills. A green box contains two $\$100$ bills and eight $\$1$ bills. A blue box contains three $\$100$ bills and seven $\$1$ bills. A yellow box contains five $\$100$ bills and five $\$1$ bills. The contestant selects a box at random and selects a bill from the box at random. If a $\$100$ bill is selected, find the probability that it came from the yellow box.
A plane's "black-box" is manufactured by only 3 companies: AirCorp, BigSkies, and CharterUS - who make 80%, 15%, and 5% of all the black-boxes made, respectively. Invariably, some of these are defective. Assuming the percentage of defective black-boxes made by AirCorp, BigSkies, and CharterUS are 4%, 6%, and 9%, respectively, find the probability that a randomly selected black-box from all black-boxes made that is found to be defective came from AirCorp.
Consider 3 coins where two are fair, yielding heads with probability $0.50$, while the third yields heads with probability $0.75$. If one randomly selects one of the coins and tosses it 3 times, yielding 3 heads - what is the probability this is the biased coin?
Suppose $P(A), P(\overline{A}), P(B|A)$, and $P(B|\overline{A})$ are known. Find an expression for $P(A|B)$ in terms of these four probabilities.
Assume the probability of having tuberculosis (TB) is 0.0005, and a test for TB is 99% accurate. What is the probability one has TB if one tests positive for the disease?
An automobile manufacturer has three factories: A, B, and C. They produce 50%, 30%, and 20% respectively, of a specific model of car. 30% of the cars produced in factory A are white, 40% of those produced in factory B are white, and 25% produced in factory C are white.
$(0.50)(0.30)+(0.30)(0.40)+(0.20)(0.25) = 0.32$
Given the calculation in part (a), we have $\displaystyle{\frac{(0.30)(0.40)}{0.32} = 0.375}$
Two manufacturers supply blankets to emergency relief organizations. Manufacturer A supplies 3000 blankets and 4% are irregular in workmanship. Manufacturer B supplies 2400 blankets and 7% are found to be irregular. Given that a blanket is irregular, find the probability that it came from manufacturer B.