Question

Haris Rauf is the star fast bowler for Pakistan. Harry Brook is a talented young batter of English

team. When Haris Rauf decides to bowl a yorker, 80% of the time he is able to execute the yorker
perfectly and 20% of the time it turns into a full toss. When Harry Brook faces a yorker, he hits it
for a boundary 20% of the time. When Harry Brook faces a full toss, he hits it for a boundary 90%
of the time. Haris Rauf is bowling the last ball of the innings to Harry Brook. Before running in to
bowl this last ball, Haris Rauf has decided to bowl a yorker, what is the probability that a boundary
will be scored of this last ball of the innings.

Answer 1

To solve it, you need to use probability. Let me show you how.

We can use a tree diagram to represent the possible outcomes of the last ball. Here is the diagram:

```

Haris Rauf

/ \

yorker full toss

0.8 0.2

/ \ / \

boundary no boundary boundary no boundary

0.2 0.8 0.9 0.1

```

The probability of a boundary is the sum of the probabilities of the branches that end with a boundary. To find the probability of each branch, we multiply the probabilities along the branch. For example, the probability of a yorker and a boundary is 0.8 × 0.2 = 0.16.

So, the probability of a boundary is:

0.8 × 0.2 + 0.2 × 0.9 = 0.16 + 0.18 = 0.34

Therefore, the probability that a boundary will be scored of the last ball is 0.34 or 34%.

Explanation: