Question

A coin is flipped to decide which team starts the game. If the probability that your team will start the game is k, then find $2k.$

Answer 1

Hint: Probability is defined as the state of being probable and the extent to which something is likely to happen in the particular situations or the favourable outcomes. Probability of any given event can be given by the ratio of the favourable outcomes with the total number of the outcomes. Here we will find the total favourable outcomes and the total possible outcomes and then will take its ratio for the required value.

Complete step by step solution:
When coin is flipped, we have total four possible outcomes-
I.When team one wins the toss and chooses to play first
II.When team one wins the toss and chooses to play second
III.When team two wins the toss and chooses to play first
IV.When team two wins the toss and chooses to play second
So, out of the total four cases it favors team one to play first then the probability can be given by -
$P(A) = \dfrac{Total \;number\; of the\; favourable \;outcomes }{Total \;number\; of \;the \;outcomes}$
$P(A) = \dfrac{2}{4}$
Common factors from the numerator and the denominator cancel each other.
$P(A) = \dfrac{1}{2}$
Also, given that the probability that the team one starts the game is “k”
$k = \dfrac{1}{2}$
Cross-multiply, where the denominator of one side is multiplied with the numerator of the opposite side.
$ \Rightarrow 2k = 1$
This is the required solution.
So, the correct answer is “1”.

Note: Consider all the possible outcomes during the flip of the coin. Initially generally held mistakes occur when the flip of coin is done there are two possible outcomes but always consider the factors for it which here is team one and team two with the outcomes of the coin so it gives us the total four outcomes. Always cross check all the possible outcomes before placing them in the formula.