Suppose the following facts to be true: $\bullet$ The probability of a random kindergartener having chicken pox at any given time is $2\%$. $\bullet$ Among kindergarteners who have chicken pox, $75\%$ have red spots. $\bullet$ Among kindergarteners who do not have chicken pox, $1\%$ have red spots. Given that Sanjay, a kindergartener, has red spots, what is the probability that Sanjay has chicken pox? Enter your answer as a fraction in simplified form.

Question

Suppose the following facts to be true: The probability of a random kindergartener having chicken pox at any given time is 2%. Among kindergarteners who have chicken pox, 75% have red spots. Among kindergarteners who do not have chicken pox, 1% have red spots. Given that Sanjay, a kindergartener, has red spots, what is the probability that Sanjay has chicken pox? Enter your answer as a fraction in simplified form.

75/124

Step-by-step explanation:

This is a question based on conditional Probability

We would solve this using Bayes's Theorem of Conditional Probability

From the above question, we have the following information:

The probability of a random kindergartener having chicken pox at any given time is 2%.

Hence, the probability that a kindergartner would not have chicken pox

= 100% - 2%

= 98%

Kindergarteners who have chicken pox, 75% have red spots.

Kindergarteners who do not have chicken pox, 1% have red spots.

The Sanjay, a kindergartener, has red spots, the probability that Sanjay has chicken pox is calculated as:

= (Probability of a random kindergartener having chicken pox at any given time ⋂ Probability of kindergarteners who have chicken pox, and have red spots)/ [(Probability of a random kindergartener having chicken pox at any given time ⋂ Probability of kindergarteners who have chicken pox, and have red spots) + (Probability Kindergarteners who do not have chicken pox and have red spots ⋂ Probability that a kindergartner would not have chicken pox)

= (2% × 75%)/[(2% × 75%) +( 1% × 98%)]

= 150/150 + 98

= 150/248

= 75/124

probability for j is 1/4

while

a is 1/6

step-by-step explanation: