Question

An urn contains forty red chips and sixty white chips. Six chips are drawn out and discarded, and a sev- enth chip is drawn. What is the probability that the sev- enth chip is red

Answer 1

Answer: The probability that the 7th chip is red = 0.4

Step-by-step explanation:

Given that;

an urn contains 40 red chips and 60 white chips

6 chips are randomly drawn and discarded and a 7th chip is drawn,

lets consider E as the the event that represent the 7th chip is red.

so probability that 7th chip is red will be;

P(E) = ⁶∑$_{i=0}$ $\left[\begin{array}{ccc}40\\i\\\end{array}\right]$$\left[\begin{array}{ccc}40\\6-i\\\end{array}\right]$ × $\left[\begin{array}{ccc}40-i\\1\\\end{array}\right]$  /  $\left[\begin{array}{ccc}100\\6\\\end{array}\right]$$\left[\begin{array}{ccc}94\\1\\\end{array}\right]$

= $\left[\begin{array}{ccc}40\\0\\\end{array}\right]$$\left[\begin{array}{ccc}60\\6\\\end{array}\right]$×$\left[\begin{array}{ccc}40\\1\\\end{array}\right]$ + $\left[\begin{array}{ccc}40\\1\\\end{array}\right]$$\left[\begin{array}{ccc}60\\5\\\end{array}\right]$×$\left[\begin{array}{ccc}39\\1\\\end{array}\right]$  + ......+ $\left[\begin{array}{ccc}4\\6\\\end{array}\right]$$\left[\begin{array}{ccc}60\\0\\\end{array}\right]$$\left[\begin{array}{ccc}34\\1\\\end{array}\right]$  / $\left[\begin{array}{ccc}100\\6\\\end{array}\right]$$\left[\begin{array}{ccc}94\\1\\\end{array}\right]$

= [ 2002554400 + ..... + 130504920 ] / $\left[\begin{array}{ccc}100\\6\\\end{array}\right]$$\left[\begin{array}{ccc}94\\1\\\end{array}\right]$

= 44821170240 / (1192052400)(94)

= 44821170240 / 112052925600

= 0.4

Therefore the probability that  the 7th chip is red = 0.4