# Math Help - Continuation of Probabililty question

1. ## Continuation of Probabililty question

Q1:
if a permutation of the word white is selected at random, find the probability that the permutatation
a.) begins with a consonant b.) ends with a vowel

Q2:
A ship has just arrive and four of its 600 passengers have contracted a rare disease. Suppose that the DOH screens 20 passengers, selected at random, to see whether the disease is present aboard ship. What is the probability that the presence of the disease will escape detection?

// I need precise and detailed solution with this problem //
Q3:
A factory produces fuses, which are packaged in boxes of 10. Three are fuses selected at random from each box for inspection. The box is rejected if at least one of these three fuses is defective. What is the probability that a box containing five defective fuses will be rejected..

I would be very happy if someone will help me...Thank you...

2. Hello, jose711!

Here's the third one . . .

Q3) A factory produces fuses, which are packaged in boxes of 10.
Three are fuses selected at random from each box for inspection.
The box is rejected if at least one of these three fuses is defective.
What is the probability that a box containing five defective fuses will be rejected?
There are: . ${10\choose3} = 120$ ways to choose 3 fuses from a box.

The opposite of "at least one defective" is "no defective" or "all good".

If the box has 5 defective and 5 good fuses,
. . there are: . ${5\choose3} = 10$ ways to choose 3 good fuses.
Hence: . $P(\text{all good}) \:=\:\frac{10}{120} \:=\:\frac{1}{12}$

Therefore: . $P(\text{at least one d{e}fective}) \;=\;1 - \frac{1}{12} \;=\;\frac{11}{12}$

3. Originally Posted by jose711
Q1:
if a permutation of the word white is selected at random, find the probability that the permutatation
a.) begins with a consonant b.) ends with a vowel

Mr F says: Apply the given restrictions to the pigeon hole principle.

Q2:
A ship has just arrive and four of its 600 passengers have contracted a rare disease. Suppose that the DOH screens 20 passengers, selected at random, to see whether the disease is present aboard ship. What is the probability that the presence of the disease will escape detection?

Mr F says: Let X be the random variable number of passengers detected with the disease.

X ~ Hypergeometric(N= 600, D = 4, n = 20).

There's an approximation to the hypergeometric distribution you're probably justified in making.

You need to calculate Pr(X= 0).

// I need precise and detailed solution with this problem //
Q3:
A factory produces fuses, which are packaged in boxes of 10. Three are fuses selected at random from each box for inspection. The box is rejected if at least one of these three fuses is defective. What is the probability that a box containing five defective fuses will be rejected..

I would be very happy if someone will help me...Thank you...
..