There are 5 traffic signals between your home and work. Each is red with probability 0.35 , independently of all others. Find: a) the probability of encountering no red lights, 2.26% 5.2% 11.6% 17.5% unanswered b) the probability of encountaring only red lights, 0.03% 0.52% 1.16% 16.4% unanswered c) the expected number of red lights you will encounter? 0.75 1.42 1.75 2.25 unanswered SubmitYou have used 0 of 4 attemptsSome problems have options such as save, reset, hints, or show answer. These options follow the Submit button.

a) 11.6%

b) 0.52%

c) 1.75

Step-by-step explanation:

For each light, there are only two possible outcomes. Either it is red, or it is not. The probability of a light being red is independent from other lights. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

There are 5 traffic signals between your home and work.

This means that

Each is red with probability 0.35

This means that

a) the probability of encountering no red lights

This is P(X = 0). So

So the answer for a is 11.6%

b) the probability of encountaring only red lights

This is P(X = 5)

So the answer for b is 0.52%.

c) the expected number of red lights you will encounter?

The expeced number of the binomial distribution is given by:

So

3 girls and 4 boys

Step-by-step explanation:

Writing the number of girls in the family as g and the number of boys in the family as b,

we know that each girl has twice as many brothers as sisters. Therefore, the amount of boys in the family (b, or how many brothers each girl has) is twice the number of the amount of girls in the family (g) minus 1 (g-1) (subtract 1 because each girl's number of sisters does not include the girl herself). We can write this as

b = 2(g-1)

Next,

we know that each boy has the same amount of brothers as sisters. Therefore, the amount of boys in the family minus 1 (b-1, subtracting 1 because we don't include the boy that has the brothers) is equal to the amount of girls in the family (g). we can write this as

b-1 = g

Therefore, we have

b = 2(g-1)

b-1 = g

Plugging b-1 = g into the first equation, we get

b = 2 (g-1)

2(g-1) = 2((b-1) - 1) = b

= 2(b-1-1)

= 2(b-2)

= 2b-4

b = 2b-4

subtract 2b from both sides to make it so that only b values and their coefficients are on one side

-b = -4

multiply both sides by -1 to solve for b

b=4

Therefore, there are 4 boys in the family and b-1 = 4-1 = 3 girls in the family.