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31 January, 02:48

Two experiments are defined below. An event is defined for each of the experiments. Experiment I: Corrine rolls a standard six-sided die. Event A: Corrine rolls a number greater than three. Experiment II: Pablo flips a fair coin twice. Event B: Pablo notes heads on the first flip and tails on the second flip. Which statement about Event A and Event B is true? A. It is not possible to determine which event is more likely. B. Event A is less likely to occur than Event B. C. Both events are equally likely to occur. D. Event A is more likely to occur than Event B.

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  1. 31 January, 03:03
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    Answer: The correct answer is option C: Both events are equally likely to occur

    Step-by-step explanation: For the first experiment, Corrine has a six-sided die, which means there is a total of six possible outcomes altogether. In her experiment, Corrine rolls a number greater than three. The number of events that satisfies this condition in her experiment are the numbers four, five and six (that is, 3 events). Hence the probability can be calculated as follows;

    P (>3) = Number of required outcomes/Number of possible outcomes

    P (>3) = 3/6

    P (>3) = 1/2 or 0.5

    Therefore the probability of rolling a number greater than three is 0.5 or 50%.

    For the second experiment, Pablo notes heads on the first flip of a coin and then tails on the second flip. for a coin there are two outcomes in total, so the probability of the coin landing on a head is equal to the probability of the coin landing on a tail. Hence the probability can be calculated as follows;

    P (Head) = Number of required outcomes/Number of all possible outcomes

    P (Head) = 1/2

    P (Head) = 0.5

    Therefore the probability of landing on a head is 0.5 or 50%. (Note that the probability of landing on a tail is equally 0.5 or 50%)

    From these results we can conclude that in both experiments, both events are equally likely to occur.
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