Hello, AlphaRock!

This is an1) A fair coin is flipped 30 times.

What is the probability the coin will show heads less than 17 times?awfulproblem!

We want the probability that the coin will show Heads:

. . 0 times or 1 time or 2 times or 3 times or . . . 16 times.

So we must find:

. .

and add them up . . .

(a) The opposite of "at least one hits the target" is "both miss the target."2) Tom has a 1/2 chance of hitting a target;

Kate has a 1/3 chance of hitting the target.

(a) What is the probability that at least one of them will hit the target?

(b) What is the probability that both of them will hit the target? (This is independent)

. .

. .

. . Therefore: .

(b) .

3) A rock concert is attended by 1300 students: 760 girls. 540.

If 4 of these students are randomly chosen to receive backstage passes,

what is the probability that at most 3 of the chosen will be boys?

The opposite of "at most 3 boys" is "4 boys."

There are: . possible outcomes.

There are: . ways that 4 boys can be chosen.

Hence, there are: . ways that at most 3 boys are chosen.

Therefore: .