Question

4. The Casino Control Commission takes a coin from a casino it suspects to be unfair....

4. The Casino Control Commission takes a coin from a casino it suspects to be unfair. They flip the coin 10 times and lands on heads 8 times.

(a) What is the probability that a fair coin would land on heads at least 8 times?

(b) Based on your answer to the last question, do you think the coin is unfair? Explain.

5. Every day, Janet either takes the bus or drives her car to work. She drives her car 30% of the time. When she drives her car, she packs her lunch 70% of the time. When she takes the bus she packs her lunch 20% of the time.

(a) Given that Janet rode the bus, what is the probability that she did not pack her lunch?

(b) Given that Janet did not pack her lunch, what is the probability that she rode the bus?

6. One fair coin and two unfair coins where heads is 5 times as likely as tails are put into a bag. One coin is drawn at random and then flipped twice. If at least one of the flips was tails, what is the probability an unfair coin was flipped?

We would be looking at Q4 here:

The number of heads in 10 tosses is modelled here as:

a) The probability of getting at least 8 heads is computed here as:

Therefore 0.0546875 is the required probability here.

b) As the probability is 0.0546875 > 0.05, therefore the event is not unusual here. Therefore we dont have evidence here that the event is unusual.