Question

Play a series of 7 chess matches. The probability that anand wins a match is 2/5 while that of carlsen winning the match is 3/5 . Assume for simplicity that the matches are independent of each other.

Answer 1

Answer:

Pls mark brainliest

Pls mark brainliest

Answer 2

Answer:

Concept:
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Step-by-step explanation:

Given:

Anand and Carlsen played a series of 7 chess matches.

The probability that Anand wins a match is 2/5

Carlsen winning the match is 3/5
Find:

1. What is the probability that Anand wins for the first time on the third match?

2. What is the probability that Anand wins exactly 4 matches (in the 7 match series)?

3. What is the probability that Anand wins the first four matches?
Solution:

Anand & Carlsen play a series of 7 matches

         $P( Anand wins )=\frac{2}{5}$

         $P (Carlsen wins) =\frac{3}{5}$

1.) Anand wins for the first time on $3^{\text {rd }}$ match

         $\begin{aligned}P &=C C A \\&=\frac{3}{5} \times \frac{3}{5} \times \frac{2}{5}=\frac{18}{125}\end{aligned}$

2.) Anand wins exactly 4 matches. Using Binomial distribution

  $\begin{aligned}P &={ }^{7} C_{4}(A)^{4}(C)^{3} \\&=7 C_{4}\left(\frac{2}{5}\right)^{4}\left(\frac{3}{5}\right)^{3}\end{aligned}$

      $=\frac{35 \times 2^{4} \times 3^{3}}{5^{7}}=\frac{\sqrt{5120}}{78125}=0.193536$

3.) Anand wins the first 4 matches

     $\begin{aligned}P &=A A A A \\&=\frac{2}{5} \times \frac{2}{5} \times \frac{2}{5} \times \frac{2}{5} \\&=\frac{16}{625}\end{aligned}$

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