In a cricket match, the probability that McGrath takes a wicket in his first over is 1/4, and the probability that Brett Lee takes a wicket in hes first over is 2/3. 11 and Lee will be starting the bowling, find the probability that at least one wicket falls in the first two overs.

Note: Round off your answer to 3 decimal places. For example if the answer is 0.5 put 0.500 and if the answer is 0.5447 them

Your Answer Here

To find the probability that at least one wicket falls in the first two overs, we will use the concept of complementary probability. 

Given:
- Probability that McGrath takes a wicket in his first over, \( P(M) = \frac{1}{4} \).
- Probability that Brett Lee takes a wicket in his first over, \( P(L) = \frac{2}{3} \).

First, let's find the probability that neither McGrath nor Brett Lee takes a wicket. 

The probability that McGrath does not take a wicket is:
\[ P(M^c) = 1 - P(M) = 1 - \frac{1}{4} = \frac{3}{4} \]

The probability that Brett Lee does not take a wicket is:
\[ P(L^c) = 1 - P(L) = 1 - \frac{2}{3} = \frac{1}{3} \]

Since these events are independent, the probability that neither McGrath nor Brett Lee takes a wicket is:
\[ P(M^c \cap L^c) = P(M^c) \times P(L^c) = \frac{3}{4} \times \frac{1}{3} = \frac{3}{12} = \frac{1}{4} \]

Now, the probability that at least one of them takes a wicket is:
\[ P(\text{at least one wicket}) = 1 - P(\text{no wickets}) = 1 - \frac{1}{4} = \frac{3}{4} \]

Therefore, the probability that at least one wicket falls in the first two overs is \( \frac{3}{4} \).

Rounded to three decimal places:
\[ \frac{3}{4} = 0.750 \]

So, the probability that at least one wicket falls in the first two overs is \( 0.750 \).

Would you like more details or have any questions?

Here are 5 more questions you might be interested in:
1. How do you calculate the probability of multiple independent events?
2. What is the difference between independent and dependent events in probability?
3. Can you explain the concept of complementary probability in more detail?
4. How would the probability change if there were more than two bowlers?
5. What is the significance of rounding off probabilities in practical applications?

Tip: Always ensure that probabilities are expressed as values between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

Explore the probability of at least one wicket falling in the first two overs of a cricket match. Understand how to calculate probabilities using complementary probability and apply them to specific scenarios involving cricket bowling probabilities.

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