Question

A and B played a game in which their chances of winning are in the ratio 3:2. A's chances of winning 3 games out of 5 game

Answer 1

SOLUTION

TO DETERMINE

A and B play a game in which their chances of winning are in the ratio 3:2. Find A's chance of winning of at least three games out of the five games played

CONCEPT TO BE IMPLEMENTED

If a trial is repeated n times and p is the probability of a success and q that of failure then the probability of r successes is

$\displaystyle \sf{ \sf{P(X=r) = \: \: }\large{ {}^{n} C_r}\: {p}^{r} \: \: {q}^{n - r} } \: \: \: \: \: where \: q \: = 1 - p$

EVALUATION

Here it is given that A and B played a game in which their chances of winning are in the ratio 3 : 2

So p = Probability of A's win

$\displaystyle \sf{ = \frac{3}{3 + 2} }$

$\displaystyle \sf{ = \frac{3}{5} }$

$\displaystyle \sf{ = 0.6}$

So q = 1 - p = 1 - 0.6 = 0.4

Now we have to find the A's chances of winning at least 3 games out of 5 game

Thus n = 5

Hence the required probability

$\displaystyle \sf{ = P(X \geqslant 3)}$

$\displaystyle \sf{ = P(X = 3) +P(X = 4) +P(X = 5) }$

$\displaystyle \sf{ = {}^{5} C_3 {(0.6)}^{ 3} {(0.4)}^{2} + {}^{5} C_4 {(0.6)}^{ 4} {(0.4)}^{1} +{}^{5} C_5 {(0.6)}^{ 5} {(0.4)}^{0} }$

= 0.3456 + 0.2592 + 0.0777

= 0.6825

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. The sun rises from north. What is the probability

https://brainly.in/question/25984474

2. probability of a 10 year flood occurring at least once in the next 5 years is

https://brainly.in/question/23287014

Answer 2

Answer:

Step-by-step explanation: