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Barbara played 25 rounds of Gorri and kept a tally of her success at hitting the target. Hits 0 1 2 3 4 5 6 7 8 9 10 Frequency 2 1 6 5 1 2 0 3 4 1 0 What is the probability that Barbara will hit the target at least 7 times in the next two rounds? (4 marks)

Question

Barbara played 25 rounds of Gorri and kept a tally of her success at hitting the target.

Hits 0 1 2 3 4 5 6 7 8 9 10 Frequency 2 1 6 5 1 2 0 3 4 1 0

What is the probability that Barbara will hit the target at least 7 times in the next two rounds? (4 marks)

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Solution

This question seems to be a bit confusing as it's not clear how many times Barbara can hit the target in a single round of Gorri. If we assume that she can hit the target up to 10 times in a single round, then the probability of hitting the target at least 7 times in the next two rounds would be calculated as follows:

First, we need to find the total number of hits Barbara made. This can be done by multiplying the number of hits by the frequency and then summing up all the results:

(02) + (11) + (26) + (35) + (41) + (52) + (60) + (73) + (84) + (91) + (10*0) = 0 + 1 + 12 + 15 + 4 + 10 + 0 + 21 + 32 + 9 + 0 = 104 hits

The total number of rounds played is 25.

So, the average number of hits per round is 104/25 = 4.16 hits per round.

However, the question asks for the probability of hitting the target at least 7 times in the next two rounds. This is a bit more complex and would require knowledge of the distribution of hits per round (which we don't have) and possibly the use of a binomial or Poisson distribution to calculate.

Without this information, we can't accurately calculate the probability. We can only say that based on her average hits per round, it seems less likely that she will hit the target at least 7 times in the next two rounds, as her average is less than 7. But this is a very rough estimate and not a precise probability.

This problem has been solved

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