Question

There are 4 rotten oranges out of 15 randomly oranges chosen what is the probability that 9th chosen is last rotten orange

Answer 1

the probability is 4/15

Answer 2

Concept:
According to the probability formula, the likelihood that an event will occur is equal to the proportion of favorable outcomes to all outcomes.
$\mbox{Probability of event to happen P(E)} = \dfrac{\mbox{Number of favourable outcomes}}{\mbox{Total Number of outcomes}}$

Students can conflate "favorable outcome" and "preferred outcome." The fundamental formula is as follows. There are, however, other formulae for various circumstances or occurrences.

Given:

Out of the 15 oranges selected at random, 4 are rotting.

Find:

What is the probability that the 9th chosen is last rotten orange.

Solution:

Let us consider up to the 9th apple. The first 8 apples should have 3 rotten ones and the remaining 5 good ones. This can be chosen in ${4\choose3} \times {11\choose 5}$ ways.

The total amount of 8 out of 15 apples chosen is $15 \choose8$.
The only rotten apple remaining is the final one, which may be chosen in only one manner.

The total number of options for choosing that one apple among the other (15 - 8 =) 7 apples is $7 \choose 1$ ways.

$\mbox{Total probability} = \dfrac{^4C_3\times ^{11}C_5}{^{15}C_3} \times \dfrac{1}{^7C_1}$

$=\frac{264}{455}= 0.58$

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