Respuesta :
Answer:
The probability that A selects the first red ball is 0.5833.
Step-by-step explanation:
Given : An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively.
To find : What is the probability that A selects the first red ball?
Solution :
A wins if the first red ball is drawn 1st,3rd,5th or 7th.
A red ball drawn first, there are [tex]E(1)= ^9C_2[/tex] places in which the other 2 red balls can be placed.
A red ball drawn third, there are [tex]E(3)= ^7C_2[/tex] places in which the other 2 red balls can be placed.
A red ball drawn fifth, there are [tex]E(5)= ^5C_2[/tex] places in which the other 2 red balls can be placed.
A red ball drawn seventh, there are [tex]E(7)= ^3C_2[/tex] places in which the other 2 red balls can be placed.
The total number of total event is [tex]S= ^{10}C_3[/tex]
The probability that A selects the first red ball is
[tex]P(A \text{wins})=\frac{(^9C_2)+(^7C_2)+(^5C_2)+(^3C_2)}{^{10}C_3}[/tex]
[tex]P(A \text{wins})=\frac{36+21+10+3}{120}[/tex]
[tex]P(A \text{wins})=\frac{70}{120}[/tex]
[tex]P(A \text{wins})=0.5833[/tex]
