1) two coins are to be flipped. the first coin will land on heads with probability .6, the second with probability .7. assume that the results of the flips are independent, and let x equal the total number of heads that result. (a) find p x = 1, (b) determine e[x].

(a) P(X=1)=0.46

(b) E[X]=1.3

Step-by-step explanation:

(a)

Let A be the event that first coin will land on heads and B be the event that second coin will land on heads.

According to the given information

P(X=1) is the probability of getting exactly one head.

P(X=1) = P(1st heads and 2nd tails ∪ 1st tails and 2nd heads)

          = P(1st heads and 2nd tails) + P(1st tails and 2nd heads)

Since the two events are disjoint, therefore we get

Therefore the value of P(X=1) is 0.46.

(b)

Thevalue of E[X] is

                     ..... (1)

First we calculate  the value of P(X=2).

P{X = 2} = P(1st heads and 2nd heads)

             = P(1st heads)P(2nd heads)

Substitute P(X=1)=0.46 and P(X=2)=0.42 in equation (1).

Therefore the value of E[X] is 1.3.

For the first question, the answer is 25/14.

Because 14x = 25y    Which means x must equal more than y. And 25/14 is the only answer like this.

For the second question, the answer is 30 x 18.

30/5 = 6     18/3 = 6      18 + 18 + 30 + 30 = 96

So, both the perimeter and the ratio is correct with this answer.

For the third question, the first answer is correct.

x < -4    and only a negative number can be less than another negative. Also, the negative must have a higher value to be less than another negative.

For the last question, the last answer is correct. no explanation for this one, it would take too long ;)