# Solving Probability Problems

Here is a more precise statement of the problem: "A family has two children. The game ends the first time that two consecutive heads ($HH$) or two consecutive tails ($TT$) are observed.

Here is a more precise statement of the problem: "A family has two children. The game ends the first time that two consecutive heads ($HH$) or two consecutive tails ($TT$) are observed.We choose one of them at random and find out that she is a girl. This problem has nothing to do with the two previous problems. I win if $HH$ is observed and lose if $TT$ is observed.If we have selected one candy from the box without peeking into it, find the probability of getting a green or red candy.

The manual states that the lifetime $T$ of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies $$P(T \geq t)=e^, \textrm t \geq 0.$$ For example, the probability that the product lasts more than (or equal to) $2$ years is $P(T \geq 2)=e^=0.6703$.

I purchase the product and use it for two years without any problems.

What is the probability that it breaks down in the third year? Given that it is rainy, there will be heavy traffic with probability $\frac$, and given that it is not rainy, there will be heavy traffic with probability $\frac$.

If it's rainy and there is heavy traffic, I arrive late for work with probability $\frac$.

On the other hand, the probability of being late is reduced to $\frac$ if it is not rainy and there is no heavy traffic.

In other situations (rainy and no traffic, not rainy and traffic) the probability of being late is [[

In other situations (rainy and no traffic, not rainy and traffic) the probability of being late is $0.25$. Here is another variation of the family-with-two-children problem [1] [7]. We ask the father, "Do you have at least one daughter named Lilia? " What is the probability that both children are girls?

What is the probability that both children are girls? For example if the outcome is $HTH\underline$, I lose.

On the other hand, if the outcome is $THTHT\underline$, I win.

In 6th grade, students begin to calculate probability.

Then, as they advance, students create models for probability questions and ultimately use probability to make decisions.

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In other situations (rainy and no traffic, not rainy and traffic) the probability of being late is $0.25$. Here is another variation of the family-with-two-children problem [1] [7]. We ask the father, "Do you have at least one daughter named Lilia? " What is the probability that both children are girls?What is the probability that both children are girls? For example if the outcome is $HTH\underline$, I lose.On the other hand, if the outcome is $THTHT\underline$, I win. In 6th grade, students begin to calculate probability.Then, as they advance, students create models for probability questions and ultimately use probability to make decisions.An outcome is the result of a single trial of an experiment.The probability of an event is the measure of the chance that the event will occur as a result of an experiment.Again compare your result with the second part of Example 1.18.Note: Let's agree on what precisely the problem statement means.Out of 32 pieces of fruit total, the probability of selecting one of the five bananas is 5/32. In a bag of colored candy, there are 11 green, 13 red, 9 blue and 2 yellow pieces.What's the probability for selecting each of the colored pieces? The probability of picking a green piece is 11/35; for red, it's 13/35; for blue, the probability is 9/35 and for yellow, it's 2/35. In a class of 30 students, 9 students prefer pizza, 2 prefer cookies, 3 prefer hamburgers, 13 prefer hot dogs and 3 prefer ice cream.

]].25$. Here is another variation of the family-with-two-children problem [1] [7]. We ask the father, "Do you have at least one daughter named Lilia? " What is the probability that both children are girls? What is the probability that both children are girls? For example if the outcome is$HTH\underline$, I lose. On the other hand, if the outcome is$THTHT\underline\$, I win.

In 6th grade, students begin to calculate probability.

Then, as they advance, students create models for probability questions and ultimately use probability to make decisions.

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