# Binomial Probability Distribution

$P(x) = {^nC_x} \, p^x \, q^{n - x}$

*n* = number of trials*x* = number of successes in *n* trials*p* = probability of success of a single trial*q* = probability of failure of a single trial

## Survival Probability Of The 6th Fly that Attempt To Pass A Spider

**Problem**

A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass. A fly is about to make the attempt. What are the chances of survival, given that five flies have already made the attempt today?

A. 1/2 | C. 3/4 |

B. 1/4 | D. 2/3 |

## 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.

## 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?

## Probability

**Probability**

For outcomes that are equally likely to occur:

If the probability of an event to happen is *p* and the probability for it to fail is *q*, then

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## Samuel Pepys Wrote Isaac Newton Asking Which Event is More Likely to Occur

**Problem**

Samuel Pepys wrote Isaac Newton to ask which of three events is more likely: that a person get (*a*) at least 1 six when 6 dice are rolled (*b*) at least two sixes when 12 dice are rolled, or (*c*) at least 3 sixes when 18 dice are rolled. What is the answer?

*a*) is more likely than (

*b*) and (

*c*)

B. (

*b*) is more likely than (

*a*) and (

*c*)

C. (

*c*) is more likely than (

*a*) and (

*b*)

D. (

*a*), (

*b*), and (

*c*) are equally likely