Question

a point is chosen in the circle at random. determine which of the statements are true. check all that apply. it is unlikely the point is in region a. it is likely the point is in region c. it is likely the point is in region g. it is impossible for the point to be in region h. it is certain that the point will land in a lettered region.

Explanation:

To solve this, we analyze each statement by comparing the area of each region to the whole circle (divided into 8 equal - sized regions, assuming from the pie - chart division):

Step 1: Analyze "It is unlikely the point is in region A"

The circle is divided into 8 regions. Region A occupies 1 out of 8 regions. The probability of landing in region A is $P(A)=\frac{1}{8}=0.125$. Since the probability is relatively low (less than 0.5), it is unlikely that the point is in region A.

Step 2: Analyze "It is likely the point is in region C"

Region C also occupies 1 out of 8 regions. The probability of landing in region C is $P(C)=\frac{1}{8} = 0.125$, which is not a high probability (less than 0.5), so it is not likely that the point is in region C.

Step 3: Analyze "It is likely the point is in region G"

Region G occupies 2 out of 8 regions. The probability of landing in region G is $P(G)=\frac{2}{8}=0.25$. Since 0.25 is still less than 0.5, it is not likely that the point is in region G.

Step 4: Analyze "It is impossible for the point to be in region H"

Looking at the pie - chart, there is no region labeled H. So the set of possible regions does not include H, which means the probability of landing in region H is 0. So it is impossible for the point to be in region H.

Step 5: Analyze "It is certain that the point will land in a lettered region"

All the regions of the circle are lettered (A, B, C, D, E, F, G). So no matter where the point lands within the circle, it will be in a lettered region. The probability of this event is 1, so it is certain that the point will land in a lettered region.

So the true statements are:

• It is unlikely the point is in region A.
• It is impossible for the point to be in region H.
• It is certain that the point will land in a lettered region.

Answer:

To solve this, we analyze each statement by comparing the area of each region to the whole circle (divided into 8 equal - sized regions, assuming from the pie - chart division):

Step 1: Analyze "It is unlikely the point is in region A"

The circle is divided into 8 regions. Region A occupies 1 out of 8 regions. The probability of landing in region A is $P(A)=\frac{1}{8}=0.125$. Since the probability is relatively low (less than 0.5), it is unlikely that the point is in region A.

Step 2: Analyze "It is likely the point is in region C"

Region C also occupies 1 out of 8 regions. The probability of landing in region C is $P(C)=\frac{1}{8} = 0.125$, which is not a high probability (less than 0.5), so it is not likely that the point is in region C.

Step 3: Analyze "It is likely the point is in region G"

Region G occupies 2 out of 8 regions. The probability of landing in region G is $P(G)=\frac{2}{8}=0.25$. Since 0.25 is still less than 0.5, it is not likely that the point is in region G.

Step 4: Analyze "It is impossible for the point to be in region H"

Looking at the pie - chart, there is no region labeled H. So the set of possible regions does not include H, which means the probability of landing in region H is 0. So it is impossible for the point to be in region H.

Step 5: Analyze "It is certain that the point will land in a lettered region"

All the regions of the circle are lettered (A, B, C, D, E, F, G). So no matter where the point lands within the circle, it will be in a lettered region. The probability of this event is 1, so it is certain that the point will land in a lettered region.

So the true statements are:

• It is unlikely the point is in region A.
• It is impossible for the point to be in region H.
• It is certain that the point will land in a lettered region.