Statistics Week 8 Graded Assignments IIT Madras

2. A and B predicts the outcomes of a cricket match and their chances of predicting the runs scored by a specific batsman correctly are $\genfrac{}{}{0ex}{}{2}{3}$ and $\genfrac{}{}{0ex}{}{2}{5}$ respectively independent of each other. If the probability of them predicting the same wrong score is $\genfrac{}{}{0ex}{}{6}{207}$. Given that they predicted the same score, find the probability that their answer is correct.

During the monsoon, it rains one-third of the days and affects students travel to school. The probability that there will be heavy traffic on a rainy day is $0.5$ and on a non-rainy day is $0.25$. If it rains and there is heavy traffic, the probability of a student arriving late to school is 0.5. If it is a clear day and there is no traffic, this probability is reduced by $\genfrac{}{}{0ex}{}{3}{8}$. In other possible situations, the probability of a student reaching school late $0.25$. If on a randomly selected day, a student arrives late to school, then what is the probability that it rained that day?

Hint: Consider the event as,
$H$= There is heavy traffic
$H^c$= There is no traffic.

There are two shops, $A$ and $B$, selling t-shirts in the market. Shop $A$ has stock of $n$ red and $2$ black t-shirts and Shop $B$ has a stock of $2$ red and $n$ black t-shirts. One of the shops is selected at random and two t-shirts are purchased from it. If both the t-shirts purchased are red and the probability that it was purchased from a shop $A$ is $\genfrac{}{}{0ex}{}{6}{7}$, find the value of $n$.