Question

In: Statistics and Probability

A bag contains 10 Cherry Starbursts and 20 other flavored Starburts. 7 Starbursts are chosen randomly...

A bag contains 10 Cherry Starbursts and 20 other flavored Starburts. 7 Starbursts are chosen randomly without replacement.
Find the probability that 4 of the Starbursts drawn are cherry.

Expert Solution

Solution:

Probability of an event E is defined as follows:

P(E) = no. of favourable outcomes/total number of outcomes

We have a bag that contains 10 Cherry Starbursts and 20 other flavored Starbursts. 7 Starbursts are choosen randomly without replacement and we have to find the probability that 4 of the Starbursts drawn are cherry. If 4 Starbursts are cherry then remaining 3 drawn Starbursts will be other flavoured.

Total number of ways of selecting 4 cherry Starbursts from 10 cherry Starbursts is,

Total number of ways of selecting 3 other flavoured Starbursts from 20 other flavoured Starbursts is,

Total number of ways in which 4 of the Starbursts drawn are cherry when the total 7 Starbursts are drawn is

Total number of ways of selecting 7 Starbursts from 30 Starbursts is,

Hence, probability that 4 of the Starbursts drawn are cherry is,

The probability that 4 of the Starbursts drawn are cherry is 0.1176.

orchestra answered 2 years ago

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