I have 20 lightbulbs in a large box. Unknown to me, 4 of these 20 bulbs are brok

Question

I have 20 lightbulbs in a large box. Unknown to me, 4 of these 20 bulbs are broken. I select 6 bulbs at random from these 20 bulbs to put in a chandelier. Answer each of the following questions separately (a) What is the chance the first bulb I pick works? 3. 20 (b) What is the chance that the second bulb I pick works? (You know nothing about the first bulb.) (c) What is the chance that all six bulbs I pick work? suppose that 25% of a certain farm's eggs contain salmonella. Are we more likely to get more than 30% contaminated eggs in a sample of 100 or a sample of 1000? Explain. (Hint: Chapter 16-Law of Large Numbers!) 4, A child opens a bag of M&Ms; and get 24 candies: 7 red, 3 orange, 5 yellow, 1 brown, 1 green, 2 blue, and 5 purple. The child chooses 2 M&Ms; at random (without replacement) and gives these 2 M&Ms; to his sister. (a) What's the chance that his sister gets two purple M&Ms;? 5. (b) What is the chance that his sister gets no purple M&Ms;? (c) What is the chance that his sister gets at least one purple M&M;? (d) What is the chance that his sister gets two M&Ms; that are both purple OR both orange?

Explanation / Answer

3. a) P(first buld will work) = 16/20

= 4/5

b) P(second bulb works) = P(first bulb will work and second bulb also will work) + P(first bulb will not work and second bulb will work)

= 16/20 x 15/19 + 4/20 x 16/19

= (16x15+4x16)/(20x19)

= 4/5

c) P(all 6 bulbs will work) = P(selecting 6 bulbs from 16 good ones)

= 16C6/20C6

= 0.2066

4. We are more likely to get 30% contaminated eggs in a sample of 100

Because, as the sample size increases, the character of sample will be more similar to that of the population.

P.S: Please post different questions separately

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