A bag contains 7 plain tokens and 5 striped tokens. All 12 tokens are equally likely to be chosen. T

Question

A bag contains 7 plain tokens and 5 striped tokens. All 12 tokens are equally likely to be chosen. Two tokens are drawn at random, one after the other, without replacement. ........ Plain ........ Striped ........ Plain ........ Striped ........ Plain ........ Striped Complete all six missing probabilities on the tree.[3] Find the probability that the first token is striped and the second is plain.[2] Find the probability that exactly one of the two tokens is striped.[2] Now suppose the first token is replaced and the bag mixed before the second draw. Calculate the probability of exactly one striped token, and compare it with your answer in (c).[2] Explain why the two draws in the original procedure are not independent.[1]

Accepted Answer

(a) First $\dfrac7{12},\dfrac5{12}$; after plain $\dfrac6{11},\dfrac5{11}$; after striped $\dfrac7{11},\dfrac4{11}$. (b)$\dfrac{35}{132}$. (c)$\dfrac{35}{66}$. (d)$\dfrac{35}{72}$, smaller. (e) Composition changes.

Two selections without replacement

Two selections without replacement

Solution:

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