Anna says that a 55% chance exists that she will go to a movie tomorrow if it is raining at noon and a 30?

Question

percent chance if it is not raining at noon. Willard forecasts a 40% chance of rain at noon. On the basis of these numbers, what is the probability that Anna will go to a movie?

Answer 1

The chance that it is raining at noon is 40% and if so the chance Anna will go to the movies is 55%. The chance she goes to the movies while raining is (0.40 x 0.55) = 0.22 = 22%

The chance that it is *not* raining at noon is 60% and if so the chance Anna will go to the movies is 30%. Thus the chance she goes to the movies while it is not raining is (0.60 x 0.30) = 0.18 = 18%

All together the total chance she will go to the movies is the sum of these two, or 40%

Answer 2

The answer is:

(0.30)(0.60) + (0.55)(0.4), where 1.0 = 100%.

In this case, that's 0.18 + 0.22 = 0.4 = 40%

You can always figure out a probability of two events happening together by multiplying their probabilities - if there's a 1/6 chance of rolling a 6 on a single die, then there's a 1/6*1/6 = 1/36 chance of rolling a six twice in a row.

Answer 3

Prob( raining and movie ) = Pr(movie if raining) * Pr( raining)

= .55 * .4 = .22

Prob( not raining and movie ) = Pr(movie if not raining) * Pr( not raining)

= .3 * .6 = .18

Pr ( movie ) = .22 + .14 = .4

Answer: 40% chance of seeing a movie

Answer 4

40%

Answer 5

60% chance that she goes