Question

Football teams toss a coin to see who will get their choice of kicking or receiving to begin a game. the probability that given team will lose the toss three games in a row is 0.125.

a. True
b. False

Answer 1

a. True

Explanation:

For each toss, there are only two possible outcomes. Either the team loses, or it wins. The probability of the team winning the coin toss in a game is independent of any other game. So the binomial probability distribution is used 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.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

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

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

Equally as likely to win or loss the coin toss(heads or tails).

So p = 0.5.

Three games

So
`n = 3`

We have to find P(X = 0). So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 0) = C_(3,0).(0.5)^(0).(0.5)^(3) = 0.125`

So the answer is true.

Answer 2

In a toss coin, the only result is a head or a tails. Therefore that ½ of the time you can win or ½ of the time you can lose. Therefore the probability of losing three games in a row is:

P = (1/2) * (1/2) * (1/2)
P = 0.125

Therefore the answer is “True”.