Hey there! I'm happy to help!
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PART A
We see that our bowler gets a strike 25% or 1/4 of the time. This means he has a 75% chance of not getting a strike. To find the probability of him getting five strikes, we use multiplication rule, which says that if you multiply the probability of one event by another it equals the probability of both events occurring.
However, this time, we have twenty separate throws, and we have to multiply all of the probabilities of a certain event happening on each roll. This means that we will multiply five 25%s to signify the five strikes and 15 75%s to represent the 15 times he misses and this will give us the probability of this event happening. I will put these in decimal form for now and then convert it back. I will also use exponents so I don't have to write out the entire thing.
P(5 strikes)=0.25^5×0.75^15≈0.000013=0.0013%
The probability of him getting five strikes is 0.0013%.
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PART B
To find the answer, we will first need to find the probability that he makes no strike at all, which will 75% multiplied 20 times.
P(no strike)=0.75^20≈0.003171211938934
We see that the percentage of the bowler getting a strike is 25%, while a miss is 75%. These add up to 100%. If these add up to 100%, then so should to probabilities of making at least one strike and making no strike at all!
100%-0.003171211938934%≈99.999682%
Basically, with twenty throws, he is guaranteed to make at least one strike with a probability of about 99.99%.
I hope that this helps! Have a wonderful day!