A public-vested party was wanting to make a court challenge to accident protection rates in one of three urban areas: Atlanta, Baltimore, or Cleveland. The likelihood that it would pick Atlanta was 0.40; Baltimore, 0.35; and Cleveland, 0.25. The gathering additionally realized that it had a 60 percent possibility of a great decision in the event that it picked Baltimore, 45% in the event that it picked Atlanta, and 35 percent in the event that it picked Cleveland. On the off chance that the gathering did get an ideal decision, which city did it in all probability pick?

An autonomous exploration bunch has been contemplating the odds that a mishap at a thermal energy station will bring about radiation spillage. The gathering thinks about that the solitary potential sorts of mishaps at a reactor are fire, mechanical disappointment, and human mistake, and that at least two mishaps never happen together. It has performed examines that demonstrate that if there were a fire, a radiation hole would happen 20% of the time; if there were a mechanical disappointment, a radiation hole would happen 50% of the time; and if there were a human blunder, a radiation hole would happen 10% of the time. Its examinations have likewise shown that the likelihood of

A fire and a radiation spill happening together is 0.0010.

A mechanical disappointment and a radiation spill happening together is 0.0015.

A human mistake and a radiation spill happening together is 0.0012.

(a) What are the particular probabilities of a fire, mechanical disappointment, and human mistake?

(b) What are the particular probabilities that a radiation spill was brought about by a fire, mechanical disappointment, and human blunder?

(c) What is the likelihood of a radiation spill?

Harley Davidson, overseer of value control for the Kyoto Motor organization, is

directing his month to month spot check of programmed transmissions. In this technique, 10

transmissions are taken out from the pool of parts and are checked for

producing absconds. Verifiably, just 2% of the transmissions have such

imperfections. (Accept that blemishes happen autonomously in various transmissions.)

What is the likelihood that Harley's example contains multiple transmissions

``13``

with assembling imperfections?

C. Fox, showcasing chief for Metro-Goldmine Motion Pictures, accepts that the studio's impending delivery has a 60 percent possibility of being a hit, a 25 percent possibility of being a moderate achievement, and a 15 percent possibility of being a failure. To test the exactness of his assessment, T. C. has planned two test screenings. After each screening, the crowd rates the film on a size of 1 to 10, 10 being ideal. From his long involvement with the business, T. C. realizes that 60% of the time, a hit picture will get a rating of 7 or higher; 30% of the time, it will get a rating of 4, 5, or 6; and 10 percent of the time, it will get a rating of 3 or lower. For a modestly fruitful picture, the particular probabilities are 0.30, 0.45, and 0.25; for a failure, the separate probabilities are 0.15, 0.35, and 0.50.

On the off chance that the principal test screening produces a score of 6, what is the likelihood that the film will be a hit?