## anonymous 5 years ago during a basketball shooting contest, each contestant gets 10 shots. for each shot he attempts, parik's probability of making a basket is 55%. What is the probability he will make at least 8 shots in his 10 attempts? express the answer as a percent. A.) 0.3% B.) 1.6% C.) 8.4% D.) 10.0%

1. anonymous

at least 8 shots means you have have to compute the probability he makes 8, 9 and 10. We are assuming the shots are independent so use binomial. $P(x=8)=\dbinom{10}{8}(.55)^8(.45)^2$

2. anonymous

i can write out the others if you like.

3. anonymous

4. anonymous

the general formula is $P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}$ i used it for n = 10, k = 8 and p=.55 for k = 9 you get $P(x=9)=\dbinom{10}{9}(.55)^9(.44)^{1}$

5. anonymous

and k= 19 you get $\dbinom{10}{10}(.55)^{10}$

6. anonymous

$\dbinom{10}{8} = \frac{10\times 9}{2}=45$ $\dbinom{10}{9} = 10$ $\dbinom{10}{10}=1$ the rest you need a calculator for.

7. anonymous

OKAY so what do i put in the caculator? im so confused

8. anonymous

oh sorry . you need to put the $(.55)^8(.45)^2$ part in the calculator because you certainly cannot do it by hand. answer is $45 \times (.55)^8(.45)^2 + 10 \times (.55)^9(.45)+(.55)^{10}$

9. anonymous

i got .0995 rounded to .10= 10%

10. anonymous

thanx so much u deserve a medal

11. anonymous

you are welcome. thank you. btw if it is not clear why this formula is the correct one let me know. it is not too hard to explain.

12. anonymous

i just have one more problem to do and im not to good with probability Karin is playing a game at an after school carnival. There are a number of table tennis balls in a bag, and 1/3 of them are marked as prize-winners. A player randomly selects a ball from the bag, checks to see if they won a prize, and then replaces the ball. If karin plays the game 12 times, what is the probability that she will win a prize exactly 4 times? A.) 0.0004 B.) 0.012 C.) 0.238 D.)0.25