Question

In: Statistics and Probability

1. A box contains four red, five blue, and eleven green lenses. One lens is randomly...

1. A box contains four red, five blue, and eleven green lenses. One lens is randomly selected from the box. is the probability that the selected lens is blue.

2. A box contains nine red, five yellow, and six green lenses. One lens is randomly selected from the box. Find the probability that the selected lens is yellow or green.

3. An unprepared student makes random guesses for the three true-false questions on a quiz. Find the probability that there is at least one correct answer.

No handwriting please type your answer.

Expert Solution

Sol 1.

Given: There are 4 Red, 5 Blue and 11 Green lenses in a box.

There are a total of 20 lenses in the box.

One lens is picked at random.

Therefore, the probability that the selected lens is blue= Total no. of blue lens / Total no. of lenses in the box

= 5/20 = 0.25

Sol 2.

Given: There are 9 Red, 5 Yellow and 6 Green lenses in a box.

There are a total of 20 lenses in the box.

One lens is picked at random .

Therefore, the probability that the selected lens is yellow or green= probability that the lens is yellow+ probability that the lens is green.

=5/20 + 6/20 =0.25 + 0.30= 0.55

Sol 3.

Given: There are 3 questions .Answer is either true or false.Therefore the probability of a question being correct is 1/2 i.e. 0.50. If we use binomial distribution to solve this, we get n= 3 , p=0.5 and q = 0.5. ( where p = probability that question is correct ,q = probability that the question is wrong and n = no.of questions)

Probability that atleast one question is correct = 1 - Probability that no question is correct

= 1 -

=1 -1*

= 1- 0.125

= 0.875

Hope I was able to answer your question.

orchestra answered 1 year ago

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