The problem states that the probability of Shalini being late for school on any day is $1/6$. (i) We need to complete the tree diagram for Monday and Tuesday. (ii) We need to calculate the probability that Shalini is late on Monday but not late on Tuesday.

1. Problem Description

The problem states that the probability of Shalini being late for school on any day is $1/6$.

(i) We need to complete the tree diagram for Monday and Tuesday.

(ii) We need to calculate the probability that Shalini is late on Monday but not late on Tuesday.

2. Solution Steps

(i) Completing the tree diagram:

Since the probability of being late is $1/6$, the probability of not being late is $1 - 1/6 = 5/6$.

For Monday:

The probability of being late is $1/6$.

The probability of not being late is $5/6$.

For Tuesday, given that Shalini was late on Monday:

The probability of being late is $1/6$.

The probability of not being late is $5/6$.

For Tuesday, given that Shalini was not late on Monday:

The probability of being late is $1/6$.

The probability of not being late is $5/6$.

So, the tree diagram should have the following probabilities:

- From the first node (Monday), one branch labeled "Late" with probability $1/6$ and another branch labeled "Not Late" with probability $5/6$.

- From the "Late" branch (Monday), one branch labeled "Late" (Tuesday) with probability $1/6$ and another branch labeled "Not Late" (Tuesday) with probability $5/6$.

- From the "Not Late" branch (Monday), one branch labeled "Late" (Tuesday) with probability $1/6$ and another branch labeled "Not Late" (Tuesday) with probability $5/6$.

(ii) Calculate the probability that Shalini is late on Monday but not late on Tuesday.

This corresponds to the path: Late on Monday AND Not Late on Tuesday.

The probability of being late on Monday is $1/6$.

The probability of not being late on Tuesday, given that she was late on Monday, is $5/6$.

Therefore, the probability of being late on Monday and not late on Tuesday is the product of these probabilities:

$P(\text{Late on Monday and Not Late on Tuesday}) = P(\text{Late on Monday}) \times P(\text{Not Late on Tuesday | Late on Monday})$

$P(\text{Late on Monday and Not Late on Tuesday}) = \frac{1}{6} \times \frac{5}{6} = \frac{5}{36}$

3. Final Answer

(i) The tree diagram is completed with the following probabilities: $1/6$, $5/6$, $1/6$, $5/6$, $1/6$, $5/6$.

(ii) The probability that Shalini is late on Monday but not late on Tuesday is $\frac{5}{36}$.