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

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