B, and C denote the events that a grand prize is behind doors A, B, and C, respe

Question

B, and C denote the events that a grand prize is behind doors A, B, and C, respectively. you randomly picked a door, say A. The game host opens a door, say B, and shoed there was Suppose no prize behind it or switching to the remaining unopened door (C). Use probability to explain whether you should switch or not. 3. Magnetron tubes are produced on an automated assembly line. A sampling plan is used periodically to assess the quality of the lengths of the tubes. The measurement uncertainty. it is thought that the probability that a random tube meets length specification is sampling plan is used in which the lengths of 5 random tubes are measured. is subject to 0.99. A a) Show that the probability function of Y, the number out of 5 that meet the length specification, is given by the following discrete probability function; fly)/5!/(v! (5-y)! (0.99)"(0.01)5-yfor y=0, 1, 2,3, 4,5 0, otherwise

Explanation / Answer

2.

If I pick a door and hold, I have a 1/3 chance of winning.

If I rigidly stick with my first choice no matter what, I can’t improve my chances.

Under the standard assumptions, contestants who switch have a 2/3 chance of winning the grand prize , while contestants who stick to their initial choice have only a 1/3 chance.

Prob. off getting the price is 1/3. and prob of not getting price is 2/3.

Because, At the beginning of the game you have a 1/3rd chance of picking the prize and a 2/3rds chance of not picking the prize. Switching doors is bad only if you initially chose the prize, which happens only 1/3rd of the time. Switching doors is good if you initially not chose prize, which happens 2/3rds of the time. Thus, the probability of winning by switching is 2/3rds, or double the odds of not switching

So, its better to switch.

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