Question

2. [6 points] Two events A, B are not disjoint. Draw the venn diag the following (shaded region indicates the expression below): a) (A ? B') ? (A ? B). b) A' ? B'. 3. [10 points] Consider an experiment with sample space S = {SSS, SSF, SFS, FSS, SFF, FSF, FFS, FFF}. Assume all outcomes are equally likely. a) List the outcomes and compute the probability for the following events A=Exactly two S. B=Exactly two F. C=At least one S. D=At most one F. b) List the outcome for events E, F. And write them as a combination of the events A, B, C, and D. E = Two or more S. F = Two or more F.

          2. [6 points] Two events A, B are not disjoint. Draw the venn diag
the following (shaded region indicates the expression below):
a) (A ? B') ? (A ? B). b) A' ? B'.

3. [10 points] Consider an experiment with sample space
S = {SSS, SSF, SFS, FSS, SFF, FSF, FFS, FFF}.
Assume all outcomes are equally likely.
a) List the outcomes and compute the probability for the following events
A=Exactly two S. B=Exactly two F.
C=At least one S. D=At most one F.
b) List the outcome for events E, F. And write them as a combination of
the events A, B, C, and D.
E = Two or more S. F = Two or more F.

2. [6 points] Two events A, B are not disjoint. Draw the venn diag
the following (shaded region indicates the expression below):
a) (A ? B') ? (A ? B). b) A' ? B'.

3. [10 points] Consider an experiment with sample space
S = SSS, SSF, SFS, FSS, SFF, FSF, FFS, FFF.
Assume all outcomes are equally likely.
a) List the outcomes and compute the probability for the following events
A=Exactly two S. B=Exactly two F.
C=At least one S. D=At most one F.
b) List the outcome for events E, F. And write them as a combination of
the events A, B, C, and D.
E = Two or more S. F = Two or more F.

Added by Derrick L.

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