The probability that exactly 6 are defective is 0.0792.
Given:
30% of the bulbs in a large box are defective.
If 12 bulbs are selected randomly from the box.
To find:
The probability that exactly 6 are defective.
Solution:
Probability of defective bulbs is:



Probability of non-defective bulbs is:



The probability that exactly 6 are defective is:





Therefore, the probability that exactly 6 are defective is 0.0792.
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Question:
The probability of a certain brand of battery going dead within 15 hours is 1/3. Noah has a toy that requires 4 of these batteries. He wants to estimate the probability that at least one battery will die before 15 hours are up.1.Noah will simulate the situation by putting marbles in a bag. Drawing one marble from the bag will represent the outcome of one of the batteries in the toy after 15 hours. Red marbles represent a battery that dies before 15 hours are up, and green marbles represent a battery that lasts longer.How many marbles of each color should he put in the bag? Explain your reasoning.
Answer:
The number of marbles of each color that should be present in the bag is;
1 red marble and 2 green marbles
Step-by-step explanation:
Here, we note that the probability of a battery going dead = 1/3 and the
Therefore if the red marbles represent that a battery dies before 15 hours then the probability of picking the red marble should be 1/3. That is if there is only one red marble in the bag, the probability of picking the red will be 1/3 when there are other 2 green batteries in the bag
That is there should be 1 red marble and 2 green marble in the bag.
Answer:
(a) Coterminal =495, -225
(b) Coterminal = 135,-585
Step-by-step explanation:
The angles are:
(a) 135° (b) −225°
The coterminal angle of angle x is derived by:

Solving (a): 135°
Substitute 135 for x in 

Split


Solving (b): -225°
Substitute -225 for x in 

Split


Step-by-step explanation:
The final balance is $12,088.87.
The total compound interest is $2,088.87.