I need quickly help Probability and Statistics questions

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1. A manufacturing plant makes radios that each contain an integrated circuit (IC) supplied by three sources A, B, and C. The probability that the IC in a radio came from one of the sources is 1/3, the sam efor all sources. ICs are known to be defective with probabilities 0.001, 0.003, and 0.002 for sources A, B, and C, respectively.
(a) What is the probability that any given radio will contain a defective IC?
(b) If a radio contains a defective IC, find the probability it came from source A.

2. You have two biased coins. Coin A comes up heads with probabaility ¼. Coin B comes up heads with probability ¾. However, you are not sure which is which so you choose a coin randomly and you flip it. If the flip is heads, you guess that the flipped coin is B; othervise you guess that the flipped coin is A. Let events A and B designate which coin was picked. What is the probability P(C) that your guess is correct? (Hint: This is an example of sequential experiments, so you might want to use tree diagrams.)

3. Assume drivers are independent.
a) If 5% of the drivers fail to stop at a red light, find the probability tahat at least 2 of the next 100 drivers fail to stop.
b) If on the average 3 drivers fail to stop at the red light during each rush hour, what is the probability that at least 2 drivers fail to stop at the red light during tonight’s rush hour?

Hello, couldi!

2. You have two biased coins.
Coin A comes up Heads with probabaility ¼. .Coin B comes up Heads with probability ¾.
However, you are not sure which is which, so you choose a coin randomly and you flip it.
If the flip is Heads, you guess that the flipped coin is B; othervise you guess that the flipped coin is A.

Let events A and B designate which coin was picked.
What is the probability P(C) that your guess is correct?
(Hint: This is an example of sequential experiments, so you might want to use tree diagrams.)

Click to expand...

\(\displaystyle \begin{array}{cccccccccc}\text{Event} && \text{Guess} && P(C) \\ \\
P(\text{coin A}\wedge H) \:=\:\left(\frac{1}{2}\right)\left(\frac{1}{4}\right) \:=\:\frac{1}{8} && \text{coin B} && \text{Wrong} \\ \\
P(\text{coin A}\wedge T) \:=\:\left(\frac{1}{2}\right)\left(\frac{3}{4}\right) \:=\: \frac{3}{8} && \text{coin A} && \text{Right} \\ \\
P(\text{coin B}\wedge H) \:=\:\left(\frac{1}{2}\right)\left(\frac{3}{4}\right) \:=\:\frac{3}{8} && \text{coin B} && \text{Right} \\ \\
P(\text{coin B}\wedge T) \:=\:\left(\frac{1}{2}\right)\left(\frac{1}{4}\right) \:=\:\frac{1}{8} && \text{coin A} && \text{Wrong} \end{array}\)


\(\displaystyle \text{Theefore: }\(C) \:=\(\text{Right}) \:=\:\dfrac{3}{8} + \dfrac{3}{8} \:=\:\dfrac{3}{4}\)