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Answer :
Answer:
P(6 times in 9 selection) = 0.116
Step-by-step explanation:
There are 11 red checkers and 5 black checkers in a bag so
P(red) = no. of red checkers / total no. of checkers = 11/(11+5) = 11/16
Checkers are selected one at a time, with replacement. So P(red) is the same for every selection at 11/16.
Use binomial distribution to find the probability of selecting a red checker exactly 6 times in 9 selections.
In this case, n = 9 and k = 6, P(red)=11/16 so
P(6 times in 9 selection) = nCk * P(red)^k * (1-P(red))^(n-k)
where 9C7 = 9! / [7!*(9-7)!] = 9! / 7!*2! = 9*8 / 2 =36
so P(6 times in 9 selection)
= 36 * (11/16)^6 * (5/16)^3
= 0.116
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Final answer:
The context is a binomial distribution where success is defined as drawing a red checker from the bag. With replacement, each draw is independent. Therefore, the formula for binomial probability can be used to calculate the probability of drawing a red checker exactly 6 times in 9 draws.
Explanation:
This is a problem of the binomial distribution. For a binomial distribution, each trial is independent, meaning the result of the previous trial does not affect the result of the next trial. This is satisfied since the question states that the checkers are selected with replacement.
'Success' in this context is defined as selecting a red checker which occurs with a probability of 11/16 (since there are 11 red checkers out of a total of 16). Failure is defined as selecting a black checker which occurs with a success probability of 5/16.
To find the probability of selecting a red checker exactly 6 times in 9 selections, we use the formula for binomial probability: P(k; n, p) = C(n, k) * (p^k) * (1 - p)^(n-k). Here, n=9 (number of trials), k=6 (desired 'successes') and p=11/16. When you substitute these values into the formula, you get the desired probability.
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