Question

Jane is a better tennis player than jack. if the probability that jane will beat jack in any given game is 0.7, what is the probability that they will each win one game if they play two games? (note that there are two ways they can arrive at this outcome: jane wins the first game or jack wins the first game.)

Answer 1

The total probability of Jane and Jack each winning one game out of two, considering the binomial nature of the problem, is 0.42.

Step-by-step explanation:

The subject of this question is mathematics, and it falls under the category of probability theory. The scenario described is a binomial problem because there are two distinct outcomes: a win or a loss. To calculate the probability that Jane and Jack each win one game out of two, we need to account for the two possible sequences of wins. The probability of Jane winning the first game and Jack winning the second is 0.7 * 0.3 (since Jack's probability of winning is 1 - 0.7 = 0.3). The probability of Jack winning the first game and Jane winning the second is also 0.3 * 0.7. Adding both probabilities together gives us the total probability for this outcome, which is 0.42.

Answer 2

Probability of Jane wins is 0.7 and probability of JAck wins is 0.3 .

So if Jane wins the first game, so we get

Probability of Jane wins * probability of Jack loose.

`0.7*0.7 = 0.49`

And if Jack wins the first game, so we get

Probability of Jack wins * probability of Jane loose.

`0.3*0.3=0.09`

So the probability that each of them win one game is

`= 0.49+0.09 = 0.58`