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...

  1. accepted if 5% of the total shipment is defective.
  2. 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...

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

 

Probability

Probability
For outcomes that are equally likely to occur:

$P = \dfrac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

 

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

$p + q = 1$

 

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.   (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
 
 
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