P - More of "What's the Probability?" Lesson

What's the Probability, cont.

At times, it is helpful for us to determine probabilities using charts. Consider the table below. A survey of 545 winter athletes asked about their favorite snow sport.

		Favorite Snow Sport
		Skiing	Snow Boarding	Tubing
Winter Sport	Cheerleading	68	41	46
	Basketball	84	56	70
	Wrestling	59	74	47

Some probabilities, we can easily determine. For instance, what is the probability of a winter athlete's favorite snow sport being skiing? Well that would be equation image indicator $LaTeX: P\left(ski\right)=\frac{68+84+59}{545}=\frac{211}{545}\approx0.387$ $P\left(ski\right)=\frac{68+84+59}{545}=\frac{211}{545}\approx0.387$

But, what if I wanted to know the probability of a person being a cheerleader, given that their favorite snow sport is skiing? Watch this video to find out:

Conditional probability of events A and B
P(B|A)=P(A and B) / P(A)

		Favorite Snow Sport
		Skiing	Snow Boarding	Tubing
Winter Sport	Cheerleading	68	41	46
	Basketball	84	56	70
	Wrestling	59	74	47

Using the chart above find the following probabilities:

1. Determine the probability that a person prefers tubing given that the person is a basketball player.

Solution: $LaTeX: P\left(tubing\mid basketball\right)=\frac{70}{210}\approx0.333$ $P\left(tubing\mid basketball\right)=\frac{70}{210}\approx0.333$

2. Determine the probability that a person is a wrestler, given that the person prefers snowboarding.

Solution: $LaTeX: P\left(wrestling\mid snowboarding\right)=\frac{74}{171}\approx0.433$ $P\left(wrestling\mid snowboarding\right)=\frac{74}{171}\approx0.433$

3. Determine the probability that a person prefers skiing, given that the person is a cheerleader.

Solution: $LaTeX: P\left(skiing\mid cheerleader\right)=\frac{68}{155}\approx0.439$ $P\left(skiing\mid cheerleader\right)=\frac{68}{155}\approx0.439$

Let's say I wanted to determine the probability of a person being a cheerleader or preferring skiing. Let's discuss how we might determine that probability.

Probability of events, A or B
P(A or B)=P(A)+P(B)-P(A and B)

Let's apply that rule to this example: Let's say you have 10 kittens, 4 are males and 6 are females. 3 males are gray, and 2 females are gray, the rest are black. Determine the probability of randomly selecting a kitten that is gray or female.

equation image indicator $LaTeX: P\left(gray\:or\:female\right)=P\left(gray\right)+P\left(female\right)-P\left(gray\:and\:female\right)=\frac{5}{10}+\frac{6}{10}-\frac{2}{10}=\frac{9}{10}=0.9$ $P\left(gray\:or\:female\right)=P\left(gray\right)+P\left(female\right)-P\left(gray\:and\:female\right)=\frac{5}{10}+\frac{6}{10}-\frac{2}{10}=\frac{9}{10}=0.9$

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