Steffi feels that the odds in favor of her winning her tennis match tomorrow are 2 to 10. What is the (subjective) probability that she will win her match tomorrow?

Question

Quizplus · Accepted Answer

The odds in favor of an event A are defined as the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

In this case, the odds in favor of Steffi winning her match are 2 to 10, or 2/10. This means that Steffi has 2 favorable outcomes (winning the match) for every 10 unfavorable outcomes (losing the match).

The probability of an event A is defined as the number of favorable outcomes divided by the total number of possible outcomes.

The total number of outcomes in this case is 2 (win or lose). The number of favorable outcomes is 2, as determined by the odds.

So, the probability that Steffi will win her match is:

P(win) = number of favorable outcomes/total number of outcomes
        = 2/2
        = 1

However, this probability cannot be greater than 1.

Therefore, we need to normalize the probability by dividing both the numerator and denominator by the denominator (total number of outcomes):

P(win) = 2/10
        = 0.2

But, we are asked for the subjective probability (the degree of belief that an individual assigns to an event), not the objective probability.

So, we can interpret the odds of 2 to 10 as Steffi believing that she will win 2 times out of every 12 times that she plays (since there are 12 total outcomes: 2 wins and 10 losses).

Thus, the subjective probability that Steffi will win her match is 2/12, or:

P(win) = 2/12
        = 0.1667 (rounded to four decimal places)

Therefore, the best answer choice is D.

Steffi Feels That the Odds in Favor of Her Winning