taiwan-gsat 2021 Q7

taiwan-gsat · Other · ast__math-b 8 marks Probability Definitions Verifying Statements About Probability Properties
A person's probability of hitting a dart each time is $\frac { 1 } { 2 }$, and the results of each dart throw are independent. From the following options, select the events with probability $\frac { 1 } { 2 }$.
(1) Throwing darts 2 times consecutively, hitting exactly 1 time
(2) Throwing darts 4 times consecutively, hitting exactly 2 times
(3) Throwing darts 4 times consecutively, the total number of hits is odd
(4) Throwing darts 6 times consecutively, given that the first throw misses, the second throw hits
(5) Throwing darts 6 times consecutively, given that exactly 1 hit in the first 2 throws, exactly 2 hits in the last 4 throws
A person's probability of hitting a dart each time is $\frac { 1 } { 2 }$, and the results of each dart throw are independent. From the following options, select the events with probability $\frac { 1 } { 2 }$.\\
(1) Throwing darts 2 times consecutively, hitting exactly 1 time\\
(2) Throwing darts 4 times consecutively, hitting exactly 2 times\\
(3) Throwing darts 4 times consecutively, the total number of hits is odd\\
(4) Throwing darts 6 times consecutively, given that the first throw misses, the second throw hits\\
(5) Throwing darts 6 times consecutively, given that exactly 1 hit in the first 2 throws, exactly 2 hits in the last 4 throws