Football teams toss a coin to see who will get their choice of kicking or receiving to begin a game. Unfortunately, the coin is not fair, and has a probability of .7 of showing up heads. If a team always guesses tails, what is the probability that they will lose the coin toss 3 games in a row?a. .027b. .125c. .343d. .657

Correct option is (c). 0.343

Step-by-step explanation:

The coin used to decide which team will receive the choice of kicking or receiving is biased.

The probability of Heads for this biased coin is, P (H) = 0.70.

Then the probability of Tails is, P (T) = 1 - 0.70 = 0.30.

A team always guesses Tails.

Compute the probability that they will lose the coin toss 3 games in a row, i.e. the toss result was Heads for 3 tosses, as follows:

P (A team losses the toss 3 times in a row) = [P (H)]³

Thus, the probability that the team will lose the coin toss 3 games in a row is 0.343.

The correct option is (c).

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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