# Probability Problem

## Duel of Two 50% Marksmen: Odds in favor of the man who shoots first

**Problem**

Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first?

A. 1/3 | C. 2/3 |

B. 1/2 | D. 1/4 |

## Probability That A Randomly Selected Chord Exceeds The Length Of The Radius Of Circle

**Situation**

If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

- Assume that the distance of the chord from the center of the circle is uniformly distributed.

A. 0.5 C. 0.866 B. 0.667 D. 0.75 - Assume that the midpoint of the chord is evenly distributed over the circle.

A. 0.5 C. 0.866 B. 0.667 D. 0.75 - Assume that the end points of the chord are uniformly distributed over the circumference of the circle.

A. 0.5 C. 0.866 B. 0.667 D. 0.75

## Probability that a Large Shipment is Accepted or Not Accepted due to Defective Items

**Problem**

A stationery store has decided to accept a large shipment of ball-point pens if an inspection of 20 randomly selected pens yields no more than two defective pens. Find the probability that this shipment is...

- accepted if 5% of the total shipment is defective.
- not accepted if 15% of the total shipment is defective.

## 1 - Probability for cars to pass through a point on road in a 5-minute period

**Problem**

The number of cars passing a point on a road may be modelled by Poisson distribution. At an average, 4 cars enters the Caibaan Diversion Road in Tacloban City every 5 minutes. Find the probability that in a 5-minute period (a) two cars go past and (b) fewer than 3 cars go past.

## Three Men Shoot and Only One of Them Hits the Target. Find the Probability that it was the First Man

## Probability: A Family of Five Children

**Problem**

A family chosen at random has 5 children. What is the probability that...

- all are girls or all are boys?
- there are 3 boys and 2 girls?
- at least 1 is a boy?